By now, John Turturro is used to being recognized as Jesus Quintana, the flamboyant, purple-polyester-clad competitive bowling maven who stares down Jeff Bridges’ “the Dude” at the lanes in “The Big Lebowski.” The chameleon-like character actor has made multiple films with the Coen brothers, Spike Lee and even Michael Bay. But when he goes out in public, people always seem to recognize him as “the Jesus.”

“If soldiers take ‘The Big Lebowski’ with them when they go overseas into battle, there’s a reason why. Something about not growing up, and living in the moment. People would all like to go to the supermarket in your bathrobe and drink out of the milk carton,” says Turturro, who’s been asked more times than he can count when the Coen brothers are going to make a sequel. (They’re not.)

But now he’s done one better: Turturro has taken matters into his own hands and spun off a film, “The Jesus Rolls,” in which Quintana isn’t just a scene-stealing cameo; he’s the main character.

“Even I didn’t get ‘The Big Lebowski’ when I first read it,” Turturro recalls. Joel and Ethan Coen kept talking to Turturro about the project, begging him to do the role. According to the actor, “I was like, ‘This is like two seconds,’ but they said, ‘Well, yeah, but you’ll do something with it.’”

And so Turturro did, licking Jesus’ bowling ball before launching it down the lane, inventing an elaborate victory dance after the character rolls a strike, and following up that bit with a hilariously inappropriate way to polish his equipment. Turturro is in the movie for just two scenes, but it’s fair to say he makes a big impression.

“If this were a concert, I’d be like the crescendo part of it,” Turturro says. “I’m like the cymbals or something.”

As it happens, the inspiration for that memorable performance predates “The Big Lebowski.” Turturro first played a version of the character at the Public Theater. “It was a trilogy of one-acts, and the character I did was based on a person I had met through the writer, someone he knew. There was something kind of disarming about the guy. He had a very gentle voice, a high voice.”

Joel Coen and his wife Frances McDormand had come to see Turturro’s show. This was back in the ’90s, and according to Turturro, Coen was reminded of the character as he was writing “The Big Lebowski.” He and brother Ethan asked Turturro to take what the actor had done on stage and combine it with another person they knew. (Most of the characters in “The Big Lebowski” were based on the Coens’ friends: The Dude was inspired by indie producer Jeff Dowd, Walter exaggerates aspects of writer-director John Milius, etc.)

And so Jesus Quintana, as fans know the character, was born.

“I’ve always thought that Jesus was a real full character, and I kind of just did the trailer version in ‘The Big Lebowski’ to serve this wonderful film,” explains Turturro. Even so, it wasn’t initially his intention to give Jesus his own movie.

While making his Naples-set feature “Passione,” Turturro encountered a couple of misfits who reminded him of the characters in French director Bertrand Blier’s 1974 cult road movie “Going Places” (liberally adapted from Blier’s own novel, “Les Valseuses”). The movie was an anarchic scandal in its day, but also a huge hit: It starred Gérard Depardieu and Patrick Dewaere as two youthful rebels who refuse to conform to the standards of bourgeois French society, breaking the law and bending sexual mores at every opportunity.

Turturro approached Blier about the idea of remaking “Going Places,” updating the story to the present day and making the duo a few decades older, so Turturro could play one of the leads. Blier signed off immediately, he says, giving Turturro permission to remake “Les Valseuses” — for a price, of course.

“I was only going to take certain parts of the book that I liked,” says Turturro, who did a draft and held a reading, but something about it didn’t work. “Then I started thinking about this character that I had originated on stage. He’s like a very deep classic underachiever who maybe never grew up, and I did a reading of the script as that guy, which seemed to work.”

That necessitated a rewrite, as Turturro made adjustments to incorporate Quintana’s ostensible qualities into the new script. There aren’t a lot of clues as to Jesus’ backstory in “The Big Lebowski,” although John Goodman’s character describes him as “a pederast” who “spent six months in Chino for exposing himself to an 8-year-old,” for example.

The movie opens with Jesus getting out of jail and reuniting with a friend (played by Bobby Cannavale) who’s also on parole. Together, they get into a series of misadventures with a range of weirdos, played by actors Turturro adores: Christopher Walken, Susan Sarandon, Jon Hamm, Sônia Braga, Audrey Tautou and Pete Davidson. Without leaning too heavily on “The Big Lebowski,” he tried to pay homage while expanding the character.

“I bowl and I dance in the movie. I figured I had to kind of acknowledge those kinds of things,” Turturro explains. “It’s funny, in the book, they do go bowling, and in Blier’s original movie, they go bowling, too. It’s a weird connection, but all of these things are that way.”

Even so, Turturro still needed to get the Coen brothers’ permission to branch the Jesus character off into another movie, but the siblings got what he was trying to do. “I showed it to Joel and Ethan, and they said, ‘Yeah, this is the right [way to go]. Just like when we did ‘The Big Lebowski,’ it needs to be its own thing.’”

Negotiations with Universal, which held the rights to “The Big Lebowski,” were a bit more complicated. “They just didn’t want me to kill the character,” he says.

As audiences will discover, Turturro has a very particular sense of humor. It’s hardly mainstream, and yet, his approach can be disarmingly sincere, which is something that defines all of his directorial efforts to date — each of which are love stories: “Mac” is about brothers, “Illuminata” focuses on the relationships within a theater company, “Romance and Cigarettes” is an homage to middle-class marriage (and Turturro’s mother in particular) and “Faded Gigolo” is a tender tale of an unconventional male escort.

These are not commercial movies in a conventional sense, but Turturro stays true to his intentions. In the case of “Romance and Cigarettes,” the wonderfully oddball blue-collar musical languished without distribution for a couple years before Adam Sandler came to the rescue. The comedian wanted Turturro for his movie “You Don’t Mess With the Zohan,” and made it a condition of Turturro’s contract that Sony release “Romance and Cigarettes.”

“The Jesus Rolls” was a similar labor of love. Turturro shot it two summers ago in New York, and tinkered with it between projects. It premieres as part of the Rome Film Festival on Wednesday, rolling into Italian theaters on Thursday in a dubbed version. This time, at least, U.S. distribution won’t be an issue: Screen Media acquired the film for a 2020 release.

Turturro hopes “The Big Lebowski’s” obsessive fans will be pleased, but sees this project as something else entirely. Whatever they make of “The Jesus Rolls” — even if they reject it outright, which is a distinct possibility, Turturro realizes — one thing is certain: He can’t tarnish the original. Come what may, the Dude abides.