You probably recognise Bill Hader, though you might not remember exactly what you've seen him in. The long-serving Saturday Night Live cast member has had supporting roles in a heap of TV and big-screen comedies over the past decade or so, from 30 Rock to Knocked Up,The Mindy Project to Trainwreck. New HBO series Barry is his biggest lead role to date, and it has the potential to be one of the best things he's ever been in.

The understated dark comedy about a depressed hitman who discovers a passion for acting was co-created by Hader and former Seinfeld (and current Silicon Valley) writer and producer Alec Berg. Hader also directed the first handful of episodes, which introduce a character with a lot more depth than the sketch show premise "hitman who wants to be an actor" first suggests.

Ex-Marine Barry Birkman fell into his career after returning from Afghanistan. He travels alone to unexotic parts of the US, efficiently murders low-level criminals, then flies, via some circuitous money-saving route, back to his grotty apartment with a Metallica poster over the bed to await his next assignment. This time his hapless handler Fuches (Stephen Root) sends him on what should be a straightforward mission: go to Los Angeles and put a hit on the personal trainer having an affair with the wife of a member of the equally hapless "Chechen mob".

Provided with an old station wagon with a booster seat in the back and a surfer bobblehead on the dashboard, Barry trails his mark to a community theatre class. But instead of doing him in, he ends up on stage performing a scene from True Romance with him. "It's LA theatre," he tries explaining to Fuches later, "I guess all the scenes they do are from movies."

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The class is taught by an enigmatic acting guru called Gene Cousineau (Henry Winkler, operating at full comedic force). His starry-eyed disciples include the always funny D'Arcy Carden (Janet from The Good Place) and Sarah Goldberg as love interest Sally. The camaraderie of the class instills a new-found sense of purpose in Barry, and he decides to take up acting while keeping his hitman day job.

Unfortunately, failure to kill his new classmate in a timely manner means there is now a messy situation with the Chechen kingpins to deal with.

These inept mobsters are the show's only major weakness - the stock standard comedy characters feel especially unimaginative next to the wryly observed theatre class. The imbalance does at least help us empathise with Hader's character as he attempts to straddle his two deeply uncomplementary worlds.

It takes a good actor to play a bad actor, and Barry is truly terrible. He only gets accepted into the class after spilling his guts out about the miserable life of a hitman to Gene Cousineau, who mistakes it for a dazzling "improvised monologue". He then turns to walk back to his car and takes eleven full steps before doing the tiniest skip of joy. It's a subtle, bittersweet and darkly funny moment - this is what the show does best.

Barry screens on SoHo, Fridays, 10pm.