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I’m early for my interview with Bill Hader, but he’s even earlier, waiting for me in his office when I arrive a very uncool half-hour before we’re scheduled to meet. I say I can go for a walk until the appointed time, but he makes a “Don’t be ridiculous” shrug and tells me to come on in. In his vintage T-shirt, dark jeans, white trainers and hair that probably should have encountered a barber at least six weeks ago, he looks closer to a 1990s video shop slacker than the multi-award winning director, writer and actor that he is, with his very own office on the Sony studios lot in Los Angeles, which is where we’re meeting today. Hader himself is pretty bemused at how things have panned out for him.

“I’m such a movie nerd that, the first time I came here, I knew that Buster Keaton had lived here, so I wanted to see that. And stage 27, where we shoot our show, that’s where they shot The Wizard of Oz. Pretty crazy,” he says, eyebrows gently rising over his mask. Despite the two of us maintaining a careful social distance, Hader and I keep our masks on throughout the interview because, due to a longstanding eye problem, he is on medication that suppresses his immune system, “which is not great right now. And then people say, ‘Getting stressed makes it worse.’ And I’m like, ‘Gee, well, I wish I could stop that,’” he says without a drop of sarcasm.

Most people in Hollywood communicate only in hyperbole (“This kale is TO DIE FOR”), while irony is the lingua franca of the comedy world. But Hader, who is from Oklahoma, has a pleasingly midwestern way of speaking, all wide-eyed sincerity expressed in a low-key manner, coupled with an occasional air of diffidence that he is the first to admit is really just him trying to manage his anxieties, keeping the surface placid while he paddles frantically beneath. In his superb TV show, Barry, which is now its third season and which he directs, writes and stars in, Hader, 43, takes his quiet earnestness and turns it into something far creepier. He plays an unknowably blank but deeply damaged hitman, who is desperate to get away from his life of crime but keeps coming back to the killing.

The show has already brought Hader three Emmys and multiple other awards. But he used to say that he could never direct himself because he couldn’t bear to look at his face. “That hasn’t gone away, to be honest. There were some scenes this season when I’m watching back and I’m like, ‘Jesus, Bill. Watch the stress eating …’” he says. But he was inspired to make Barry after visiting the set of Better Call Saul, and Barry shares some of that show’s ingredients: off-kilter humour, sharp dialogue mixed with extreme violence, a propulsive plot and a fascinating central character.

“From the start, I said, ‘I want to explore the version of the disease that’s in Barry, that’s also maybe in everybody. That thing that makes us keep making bad choices, so let’s explore that?’ And people would say, ‘OK, but, umm, it’s a comedy, right?’” he says and laughs.

Barry is definitely a comedy, but pretty much none of it comes from Barry himself, even though Hader is one of the most enjoyable comedic actors around, the kind you’re always happy to see pop up in a movie. He went from being a total unknown to a genuine star in his eight years on Saturday Night Live (SNL), where he was known for his impressions, and he brightens up good comedies in small roles (Superbad, Tropic Thunder), and redeems so-so movies in big roles (Trainwreck). In Barry, the comedy largely comes from the people in Barry’s drama class, which he attends in the hope of swapping killing for acting. Had he grown tired of playing the funny guy?

“No, not at all – it’s always about what serves the story. But also, I’m not that great at writing big characters for myself and I tend to get excited about the other characters. Once HBO sent us a note saying, ‘But Barry’s not in this episode.’ I was like, ‘Oh, you don’t need to see him!’ But they were like, ‘No, we kinda do …’ And that’s not false modesty from me, or whatever. It’s just, I’m happy moving towards the thing, not being the thing,” he says.

The best thing about Barry is often Barry’s acting teacher, Gene Cousineau, played by Henry Winkler, reputedly one of the kindest men in the business. Does Winkler ever call him after getting the script and say, “Gee, Bill, there’s a lot of killing this week …”?

“He gets uncomfortable, but he’s always very sweet about it. He’s said that some of the stuff we’re doing in the new season is the most intense he’s ever done in his career, and that’s because we always try to get to some emotional truth and show the consequences of violence, whether emotional or real. So, as weirdly dark as people say the show is, I feel like, in our writers’ room, we’re being very empathic and asking, ‘Well, how would that make those people feel, if that happened to them? What’s the honesty?’”

I ask if he’s ever seen that clip of when a BBC reporter asked Winkler – not realising who he was – about his thoughts on Heathrow’s proposed expansion. Winkler replied solemnly and thoughtfully: “Let me ask you a question: would that bring more people to the economy?” Hader giggles – he has a great giggle – and says no. “But that is totally him. If someone comes to him with a problem, he gets very involved. Like, ‘What is happening? This is terrible! You need to watch out for that!’” he says, suddenly morphing into Winkler, just as he used to turn into John Malkovich, James Carville and Jabba the Hutt on SNL.

Hader was so good at doing impressions back then that I assumed it was his way of hiding himself. And it was a bit, because he would get so anxious about performing on live TV that he suffered occasional panic attacks. He had never even done any celebrity impressions until his SNL audition, when he suddenly decided maybe he could be “the impressions guy”, like his comedy hero, the late Phil Hartman, also a former SNL star, and also a man whose earnestness could shade into blank unknowability.

But then, in 2014, I saw the film The Skeleton Twins, which made me realise that Hader’s impressions actually revealed something else about him: he’s a very good actor. In that film he plays Milo, a depressed actor, who, after trying to kill himself, goes to stay with his estranged twin sister, Maggie (Hader’s SNL colleague Kristen Wiig.) Hader is extraordinary in this, somehow looking like an entirely different person than the comedian he was on SNL, despite not altering his appearance at all. His every gesture, every flicker of expression, feels entirely true to Milo, a young man confident in himself but broken by the world.

“I loved being in that movie,” he says with real feeling. “I’d been wanting to do something different for a while, but I was only being in comedies. So I did a table-read and, yeah, that was really great.”

As well as being depressed, Milo is gay. So was one of Hader’s most beloved characters on SNL, Stefon, a New York tour guide whose only recommendations are terrible nightclubs (“Located in a haunted synagogue, this upper lower side hotspot is the creation of Italian reggae singer, Rasta Primavera”). Given the debates about which actors can play which roles, would he think twice now about playing those characters?

“Oh, um, right. Well, Craig Johnson [the director of The Skeleton Twins] is gay, and he asked me if I’d be interested in doing that movie, and maybe that wouldn’t happen now. And that’s OK. But I really did love playing those characters, and I hope that when people saw them, they saw them as human beings,” he says.

He’s not exactly reluctant to answer the question, but the diffidence has returned, which suggests to me he wants to move on. But 10 minutes later, he comes back to the subject and says SNL recently “floated” the idea that he come back to play Stefon.

“I was like, ‘I don’t think that’s really a good thing to do now.’ I mean, we had an openly racist, homophobic and misogynistic president, and half the country voted for him – twice! So [those attitudes] are really prevalent. That was a big eye-opener for me and it made me back up a bit and say, ‘Wait, maybe people see this character a different way.’ Because I really love Stefon and it never occurred to me that he would be seen as a stereotype, and that really hurt,” he says.

I tell him I had a similar recent re-evaluation of Superbad, in which Hader played a police officer. I loved the film when it came out, especially how it poked fun at the clueless sexism of the boys (played by Jonah Hill and Michael Cera). But, during the Trump era, those jokes about menstrual blood and blowjobs felt degrading rather than knowing. On the other hand, that is probably how teenage boys talk.

“Right, so then you ask, ‘Is this just the honesty of these kids?’ But the thought that anyone might think I was making fun of gay people really sucks. So I’m not saying I’d never play those characters again, but not today,” he says.

Hader grew up in Tulsa, Oklahoma, the anxious eldest kid in a family of five. “I was always waiting for the shoe to drop so I could never enjoy things in the moment, only in retrospect. Then I could be like, ‘Oh, nothing bad happened. I guess that was fun!’” he says. In high school, he fully embraced his film nerd identity and dropped out of the sports teams. “It was a nice form of rebellion: ‘Everyone’s going to the football game but I’m going to watch Aguirre, the Wrath of God. All alone, in my house. That’ll show ’em!’”

Hader dropped out of college and moved to LA with some friends. He jobbed around as a PA on film sets and did some comedy with friends, one of whom was the brother of Nick Offerman, a star of Parks and Recreation. After Offerman’s wife, Megan Mullally, saw them perform, she recommended Hader to SNL’s creator and producer, Lorne Michaels, and that was that. “Megan totally changed my life. Without a doubt, I would not be here without her,” he says.

The downside to being here is that annoying journalists ask questions about his private life. Hader has three daughters, aged seven to 12, and got porced from their mother in 2018. Soon after he was dating Rachel Bilson, AKA Summer from The OC, and is now reported to be dating Anna Kendrick. When you’re famous, does it make things easier to only date other famous people? He makes a rueful laugh: “That’s a hard one to answer, especially with having kids, because they’re at the age when they see things. So I understand why you asked that, but I’m kind of private. Like, I don’t even have any social media,” he says.

Why not?

“It just feels like there are a lot of opinions, and that’s not a thing I was ever interested in. Also, I’m often in the wrong. I’ll say ‘I think this’, then someone else will say, ‘What about this?’ And I’ll be like, ‘Oh yeah!’” he says, and laughs.

I tell him that Barry is like the opposite of the late night shows in which the host shouts his opinion at you, because it’s so subtle.

“Yeah, I just like narrative stories, and afterwards you can go: ‘Jeez, that was very challenging, but I think I got something out of it.’”

What does he hope people get out of Barry?

“Oh! Um,” he says, alarmed at being asked to nail his colours to a post. But he soon warms up. “Well, I hope they’re entertained. And maybe also they ask, ‘Is it possible to change your nature?’ Because that’s something we keep coming back to. And how much of us go to unhappiness, because I wish I could wave a magic wand and not be anxious all the time, but instead you just go, ‘Oh God, I have to manage it.’”

But has he changed his nature? Is he less anxious these days?

“Well, when I’m doing all the stuff for the show, you can’t overthink things, which is good. And when the worst happens, you learn to cope, like this thing with my eye. There’s nothing you can do, so you deal with it. And when things get overwhelming, you think to yourself, hey man, this is pretty awesome. I used to be a PA and deliver coffee to people here. Now I have an amazing job and I’m being interviewed by the Guardian here. Really cool. Like, I can’t complain much,” he says, and he looks almost like he’s enjoying the moment.

Barry is on Sky Comedy and streaming service NOW.