John Turturro is much less tortured than I was expecting. One doesn't like to get performers too mixed up with their roles, but I can't get the image of him as Barton Fink, the tortured playwright caught in a long dark night of the soul in the Coen brothers' Palme d'Or-winning comedy of 1991, out of my head. Of all the Coens' patsies, Turturro played put-upon best, and in roles for Spike Lee and Robert Redford he seemed to specialise in the kind of guys – embattled, tightly wound, thin-skinned – who draw injury from the universe like lightning. That high-rise 'fro seemed frazzled with bad karma.

The curls are speckled with salt and pepper, these days. A wiry 57, he arrives for lunch at Bar Pitti on Sixth Avenue, New York City, looking debonair in a cashmere Canali sports jacket. Posing for a photo with a fan on the way in, he is guided to a corner table of the restaurant by its owners, who greet him on first-name terms. "If I come here I know what I can get with the kind of cooking it is," he says as a waiter arrives bearing a blackboard of specials. Turturro likes his neighborhood joints. He gets his coffee from the same Puerto Rican coffee house on Park Slope, Brooklyn, every morning, and gives money to his favourite downtown cinema, Film Forum.

He's a little nervous: his latest movie, Fading Gigolo, which he wrote, directed and stars in, has just added 100 cinemas to its release in the US. "I was on the phone all day yesterday saying, 'That's too much,'" he says. "But all the theatres want it. People are enjoying the movie so much. I'll have the plate of asparagus please."

Comedy team … Woody Allen and John Turturro in Fading Gigolo. Photograph: Jojo Whilden

Turturro plays a middle-aged Brooklyn florist who is pressed into service as a gigolo by his friend, a bookseller played by Woody Allen. You read that right: Woody Allen is John Turturro's pimp. The two find a wonderful comic rhythm together, with Allen mounting one of his speediest displays of shtick in years – arm waving, stammering, eyebrows a-pogo – while Turturro plays it straight, his character a zen-master sensualist, bringing his healing powers to the lives of the women he touches: Vanessa Paradis, Sharon Stone, Sofía Vergara. Maybe it's his Italian side – his family are originally from Sicily and in 2010 he made a terrific documentary about the music of Naples – but Turturro turns out to be an unexpected cheerleader for abbondanza and passione.

"Everybody has their own individual sexuality, sensuality," he says. "There are people like Jeanne Moreau or Judi Dench who have this fascinating sexuality to them. They are not beauties, really, but sometimes people who are really beautiful do not actually have that much sexuality. I am not saying I do, by the way. The title of this film could have been Not Too Pretty, easily. I'm just saying that sometimes they are so used to receiving attention and not giving it or listening or holding it. I do not see a lot of movies that have sensuality. I can go to a Wes Anderson film and appreciate it, but it is completely sexless."

Has he ever been in a threesome? It's not the sort of question one asks movie stars usually, but talking about one of the scenes in the film, a faltering encounter between him, Stone and Vergara, he sounds so knowledgeable that it just sort of pops out. "Once, back in the 70s," he replies, matter-of-factly. "I was a certain age in the 70s, people were trying all kinds of stuff, it was before Aids. I was younger. It was awkward. People do that, they say, 'Let's have a threesome,' and your brain is going 'yeah yeah', and then they go, 'Dude, this is a fucking disaster… This is not what I thought it was going to be.' People get jealous, this and that."

The sensualist … John Turturro in Fading Gigolo. Photograph: Jojo Whilden

With its nods to the movies of Woody Allen and Spike Lee, its old-school neighbourhood humour, and Brooklyn locations photographed in a beautiful amber light by the Italian cinematographer Marco Pontecorvo, the film seems to evoke a honeyed parallel universe in which the indie film movement of the 90s that bore Turturro to fame is still in rude health. Its genesis couldn't have been less Hollywood: Turturro pitched Allen through his barber on 57th street, Anthony, whom both men use. "I think he also used to cut Al Pacino's hair," he says. "I said, 'Listen, you do not have to say anything to Woody, if it comes up in conversation …' I was kidding around. There was no script. I just had the idea. He said to Woody, 'John came up with this movie, can I talk to you?' I was so shocked when he called me. He said, 'Why don't you write it and I will give you feedback?' He said, 'You are going to direct it?' I said, 'Yeah, is that all right?' He goes, 'Yeah, fine.'"

There followed a series of passes at the script with Allen providing notes as they went, which amounted to a masterclass in the art of comic screenwriting. "He sent me these voluminous emails which I would lay down to read. Woody would tell me, 'I hate this … I hate this … I hate that … I like this.' He saw that I could take his withering criticism. He encouraged me to read some Isaac Bashevis Singer. I really got to know him way better than most actors who have worked with him, except the ones who have worked with him 10 years."

This brings us uncomfortably close to the issue that seems to dog Allen's collaborators these days: the renewed allegations of sexual abuse made by Dylan Farrow during the recent Oscar season. Was the distributor worried that audiences might stay away from a sex comedy with Allen in the role of pimp? "It's an old story, and it came up way after I made the movie," says Turturro. "The movie was finished and sold everywhere. People made up their mind a long time ago, as most people do. There may be a small percentage that changed, but it hasn't stopped people from going to the movie."

On a happier note, Turturro's barber is getting a small percentage for his role as facilitator. Executive producer credits have been built on less. "Are you kidding me? Absolutely. It's one of those old-world communications. Someone actually has to cut your hair. It can't be an app. Eventually we'll have an app. You'll take it and you'll go, 'Erm,' and it will be gone. That will be it." He flags down the waiter. "Hi, can I have a macchiato please?"

He'd like to move quickly on his next film. "I would like to be able to flex my muscles a little bit, or develop my muscle because then you get less precious about it. I'd love to make a movie about jazz musicians who never made it. Not a story about triumph, but about those guys who are always thinking, 'We're going to have a breakthrough.' I've been thinking about Clint Eastwood. I'm thinking about him and Woody."

I can see the poster now, I tell him. "They'd be in a band, a real band, they'd have to play the songs," he continues. "Am I Blue? Or something like that, Rodgers and Hammerstein, one guy does the lyrics, one guy does the music. They'd have to be a band that does covers, old classic songs. Maybe they lose their singer. I'll direct, but the only actors in the movie would be directors. Get Marty to play the manager."

He's already approached Eastwood. "We floated the idea out to him and he was laughing."

Fading Gigolo is released on 23 May.