When considering the public image that Hugh Jackman has spent an illustrious three-decade career cultivating, it helps to focus on a red carpet incident from 2013. Jackman’s at the Zurich film festival for the gala screening of Prisoners, where he runs into a familiar face in the press scrum outside the theater.

“Rollo!” Jackman says, his eyes lighting up in recognition; he’s identified Rollo Ross, a Los Angeles-based reporter and Jackman’s former phys-ed student from his days as a stand-in teacher during his gap year at Uppingham school in 1986. After nearly 30 years, Jackman identifies his former pupil and greets him as if they’re old friends, playfully ribbing him about maintaining his standards of physical education. He’s charm incarnate – too congenial and thoughtful to possibly be real. What human being remembers everyone they’ve ever met?

In the superb new HBO movie Bad Education, Hugh Jackman’s character starts to seem like another endearing illusion around the time that he does this exact same thing. Frank Tassone, the superintendent presiding over Long Island’s Roslyn high school and the No 4-ranked district that contains it, gets a drink from a bartender who happens to have once strode Roslyn’s halls. Tassone duly recalls not only the boy’s name, not only that he used to like writing science-fiction stories, but one of the plots dreamed up by his teenaged self.

Except this isn’t a scholastic administrator showing his dedication to the job. This is the beginning of a flirtation between the two men, and in a greater sense, the beginning of the end.

Cory Finley’s film tracks Tassone’s downfall, a scam of such hubris, folly and tragedy that it fits snugly in the Greek pantheon. Tassone skimmed millions from the school district budget to maintain a princely lifestyle with a husband unbeknown to everyone, from the co-workers buying his story about a deceased wife to the aforementioned boytoy kept in the dark. The ripped-from-the-headlines true story would be engrossing any way you slice it, but Jackman elevates the facts into a sublime dramatic work.

That’s not just because he gives the performance of his career, more studied and specific and fully-formed than we’ve ever seen, but because he brings an abundance of extra-textual baggage. The film confronts head-on the question of “Hugh Jackman”, the intuited public perception halfway between the real Jackman and his fictionalized persona of Tassone. The answer to this question, unsurprisingly, is complicated.

Jackman and Tassone excel by carefully maintaining an aura of absolute control. Frank Tassone is the sort of guy who makes the phrase “not a hair out of place” literal, with his sleek mane so raven-black it just has to be dyed. He’s introduced slugging activated-charcoal smoothies, part of a fitness regimen so obsessive we eventually learn regular facelifts help keep him in tip-top shape. That’s one of the first signs his total composure might be hiding something, as if behind the facade of cufflinks and cologne spritzes there’s only a big nothing. He uses his charisma to keep the world at an arm’s length, letting them see only the version of himself he’d like them to.

Even before The Greatest Showman made it official, Jackman was a consummate pro of stage and screen. He’s a paragon of excellence, the night-after-night dependability that made him a sensation on Broadway, where a person needs an entertainer’s soul and an athlete’s hustle to get by. Not even years of reprising his star-making Wolverine gig could make him seem rugged; his has always been a clean-cut machismo, polished to a sheen. This quality, combined with Jackman’s tendency to play personal matters close to the vest in interviews, has led some fans to see him as perhaps too perfect to be true. Jackman’s not one of those tell-all A-listers making content out of his privacy; he comes off like a movie star in the old Hollywood tradition, a seeming trick of the light, as much PR team as man.

Adding another fascinating wrinkle is Tassone’s homosexuality, kept to himself while not strictly closeted. This may be the gentlest and most vulnerable Jackman has ever permitted himself to appear on screen; one scene deals the veteran hoofer his greatest acting challenge by forcing him to be bad at dancing, having followed his younger boyfriend to a club where they at-first-tentatively get close to Moby’s In This World.

Watching Jackman shed his self-consciousness and allow Tassone to relax for the first time in the film lands with a disarming tenderness, in part because he’s nodding to rumors in our real world. Though he’s been married for years, Jackman still attracts murmurs, and he must have known this when agreeing to take this job. It would be more than a reach to describe the performance as confessional, but it cannot be denied as commentary.

Jackman finds the humanity in someone who’s forced himself to bury his down deep, for the sake of fitting into a rigid template of success. The brutal irony is that Tassone probably could have been openly gay if he wanted to – even in 2002, Long Island was pretty tolerant – but he forced himself to match a picture of a superintendent he had in his head. Perhaps not in regard to his sexual orientation, but Jackman has also conducted himself with an unflappable professionalism, fitting himself into a classical mold of movie stardom. As much as it has won him a massive fandom, it’s also rendered him somewhat unknowable to the sort of cinephile curious about the overlap between an actor’s work and self.

With his latest and greatest acting feat, however, he’s teased us with a couple of clues as to what happens when someone who’s always “on” finally goes off stage.