J.K. Simmons was reluctant to appear in “Being the Ricardos.” But reading Aaron Sorkin’s script, “I was able to see the gift that Aaron was giving to each of the actors.”

It’s a gift exchange: Simmons is so versatile and talented that he brings gifts to any filmmaker he works with.

Oscar voting runs Jan. 27-Feb. 1. Simmons has been getting some awards buzz, but deserves more: As an actor, he has the blessing/curse of always making it look easy so he’s sometimes taken for granted. But with “Ricardos,” as with everything else, he seems so perfect that you can’t imagine anyone else playing the part. He’s definitely a supporting-actor contender.

Simmons and Sorkin go back to 1990, when the actor was an understudy in the Broadway production of Sorkin’s breakthrough “A Few Good Men.” When Simmons stepped into the role, a producer urged Sorkin to come watch. Sorkin was impressed and now says he wants the actor in every movie he makes. (Amazon’s “Being the Ricardos” is Sorkin’s third film as director and his 10th as a writer.)

When Simmons first heard about “Being the Ricardos,” he says, “I wasn’t all that interested, despite Aaron’s involvement. I’ve always been reluctant to portray real people, especially 20th century people who have been in the public eye.” But Sorkin emphasized, “We’re not interested in mimicry; we’re interested in who these people are.”

Simmons says, “That was all the reassurance I needed to get over my fear. It was a scary prospect for all four of us to play these iconic people,” he says, referring to Nicole Kidman, Javier Bardem and Nina Arianda as, respectively, Lucille Ball, Desi Arnaz and Vivian Vance. Simmons plays William Frawley and smiles,“Obviously I’m very glad I did the film.”

He started doing research.

“I wanted to honor William Frawley — who he was and wasn’t. So it was a different kind of preparation than I usually do. To me, the inner life is what’s paramount. I worked on that, and it was important to get at the heart of who he was.

“I think we all have at least one friend who’s an absolute nerd for all things ‘I Love Lucy.’ Alan Filderman, a New York casting director who’s a friend, called and said, ‘I have six books you need to read and I want to tell you everything I know about William Frawley.’ That’s where my research started.”

Among other insights, “Alan told me Bill Frawley’s hands often shook. As I watched old episodes, I realized that whenever you see him standing there, he’s protecting his hands. He’s got his hands in pockets, or folded in front of him, hands firmly on his hips. He never lets himself be vulnerable, by letting the audience see his hands shake.”

After the initial table read for each episode, Frawley discarded every page of the script that he wasn’t in. He would tuck his pages in one pocket, with the racing form in the other. “I found that to be a gem of insight into him. I did the same thing with my ‘Being the Ricardos’ script. It was an interesting exercise in helping to create my own connective tissue between all of my scenes.”

Simmons seems to have endless range as an actor.

He did years of stage work, describing the life of an actor as “rejection after rejection after rejection.” But among his Broadway successes were Neil Simon’s comedy “Laughter on the 23rd Floor,” plus singing and dancing in “Guys and Dolls” (as Benny Southstreet) and “Peter Pan” (playing Captain Hook). He also made his mark for years Off Broadway and in regional theater.

He “accidentally made a segue to screen acting,” he says, with dozens of roles including cops, criminals, psychos and psychiatrists.

Aside from an appearance in Sorkin’s series “The West Wing,” he was a scary prisoner in “Oz,” a doctor in “Law & Order,” the loving dad in “Juno,” plus the genial spokesman for Farmer’s Insurance and his award-winning work as the overbearing teacher in the 2014 “Whiplash.”

In 2021 alone, aside from his supporting role in “Ricardos,” he was in “Ghostbusters: Afterlife,” played Commissioner Gordon in “Zack Snyder’s Justice League” and was muckraker J. Jonah Jameson in the blockbuster “Spider-Man: No Way Home.”

Simmons is happy to talk about “Being the Ricardos,” but seems more comfortable talking about the work of others, rather than his own. He says 64 actors have billing in “Ricardos,” and they’re “remarkable.”

He reserves special praise for Sorkin. “He’s such an actor’s writer. Everyone knows him as a giant intellect, but they sometimes oversimplify it and say ‘Oh, yeah, all the characters will be super-smart and talk fast.’ We all know his brain. But as an audience, and as an actor working with him, it’s also his heart that makes him a great writer.

“I hope this is the first of many times we get to work together.”

That seems a safe bet. So the next step is in the hands of Oscar voters.