One otherwise ordinary day in southern Spain, where I went to meet Oscar Isaac, I was woken by the sound of a marching band in the street outside my hotel room. Going to the balcony, I found, for no apparent reason, a procession of Stormtroopers, Jawas, and other assorted baddies, brought up in the rear by Darth Vader, like Santa in the Macy's Thanksgiving Day Parade. Several hundred people were watching while the band played “The Imperial March.” I had assumed it was traditional folk music. And, of course, in a very real sense it was.

I did not know if the sound carried to wherever Oscar Isaac was at that moment. If it did, I wondered if some part of him shivered. To become part of Star Wars is less like joining a cast and more like joining a priesthood. It made perfect sense that the final trailer for the newest episode, The Force Awakens, aired at halftime of a Monday Night Football game, the NFL being another multi-billion-dollar corporate enterprise that has turned the neat trick of getting itself treated as a sacred public institution. (Not to mention the shared fetish for Roman numerals.) Isaac, meanwhile, has made his growing name in a series of brilliant but darkly idiosyncratic roles: the brooding businessman so vain about his integrity that it becomes its own kind of corruption in A Most Violent Year, or the wounded, wandering folk singer of the Coen brothers' Inside Llewyn Davis. Even his sci-fi debut, as the cerebral sex-robot-building Frankenstein of Ex Machina, was high on discussions of the nature of consciousness, low on explosions.

*FANBOYS: We can’t actually say whether he’s a Jedi or not

Moreover, he has shown himself to be a lifelong non-joiner and an actor so private about his private life that the mere use of the word girlfriend leads him to try to take it back the next day. And now Oscar Isaac is about to join the biggest, most scrutinized club in the world.

To which the actor responds in pretty much the only way he can: with a shrug. “Obviously I think a lot of people are going to see Star Wars,” he says. “I imagine I might get recognized more. But right now it's still sort of an abstract idea. And, to be honest, that's something people tell you for a long time. Like, every other movie: ‘Here it comes! Here it comes! You better be ready!’ ”

It is notoriously difficult to be too late to eat dinner in Spain, but Isaac is pushing it. His plane was delayed three hours in Malta, and now it's approaching midnight as we hurriedly cross the Plaza de Gracia in Granada. The tables set up beneath lights strung from the trees are still filled with boisterous families sipping sherry, finishing dessert, and otherwise enjoying a cool Saturday night in October, but kitchens are beginning to close, and we get a subdued eye roll as we squeeze into two seats at the counter of a brightly lit seafood-tapas joint. Nevertheless, glasses of manzanilla soon appear, followed by a parade of lustrous pink shrimp, ruby-red-tipped clams, and deep-fried sardines. This last presents a challenge.

“Do you really eat the head?” Isaac asks. I do, I tell him. With the slightest hesitation, he follows suit, chews, and swallows.

“Now, that's good head,” he says. We look at each other. I close my notebook. “Well,” he says. “There's your story.”

Isaac orders a bottle of Rioja in fluent Spanish. Born in Guatemala to a Cuban father and a Guatemalan mother, he grew up in Miami. With his heavy-lidded eyes, angular features, black fedora, and hair and eyes so dark they could be inkblots in a pictogram, he looks about as natural and old-world in this setting as a figure on an old vermouth poster.

The 36-year-old actor has been in Spain and Malta for almost three months, shooting The Promise, a love story set against the backdrop of the Armenian genocide and collapse of the Ottoman Empire. (“A big hootenanny,” he says drily.) Before that, it was Montreal for three months, working on X-Men: Apocalypse, in which, entombed in so much prosthetic gear he required a built-in cooling unit, he plays the eponymous Apocalypse. (That's a bad guy, in case the subtlety of the name fooled you.) He won't set foot in the United States until Christmas; won't see his apartment and dog, in Williamsburg, Brooklyn, until February. Nobody would confuse it with coal mining, exactly, but it is a peripatetic, almost entirely work-focused life, and he is feeling it. “I do miss home,” he says. “And it's not like there's an endless well to draw on. Inspiration has to come from somewhere—observing things, reading things, thinking about things. I get a bit nervous I'm not doing that.” Small comforts help: bringing plants into hotel rooms, the guitar he keeps close at hand. And he's also aware of Hollywood's mercurial attention span: “These things go up and down. There's a sense of ‘Strike while the iron is hot.’ ”

In person, Isaac has a wide, easy smile that serves as a reminder of how elusive it's been on-screen. It's been a long time since we've had a leading man whose charisma comes packed with such tetchiness, so little naked desire to be liked. Isaac's most memorable characters have all projected varying degrees of menace and loneliness. A Juilliard grad, he is scholarly and passionate about acting, deeply romantic about its artistic possibilities. Inevitably you think of De Niro, Pacino, Hoffman, Hackman. Call it, apropos of nothing in particular, the pre*–Star Wars* generation.

To become part of ‘Star Wars’ is less like joining a cast and more like joining a priesthood.

It was precisely that quality, though, that led Star Wars director J.J. Abrams to summon Isaac to a meeting in Paris in March 2014. A fan of Llewyn Davis, Abrams was convinced that Isaac was the actor needed to play the role of the roguish fighter pilot Poe Dameron, a character the director describes as “wonderful, daring, sardonic, brave, loyal.” (When it's pointed out that this description sounds an awful lot like Han Solo, Abrams is coy: “I would like to think there's room for more than one rogue in Star Wars.”)

Nathaniel Goldberg

In Paris, the two met at the famous Café de Flore, where Abrams patiently sipped a coffee while Isaac read scenes from the movie on Abrams's iPhone. Then they talked into the night about the story and what the role might become.

“J.J. basically told me it was an intense, heroic, dramatic character and he hadn't seen me do that,” Isaac says. Nevertheless, he hesitated. “I didn't know if I could make it interesting,” he says. “I didn't know why me and not anybody else.” Only after flying home and thinking it over for a few days did he decide to take the plunge.

Abrams was delighted. “Oscar is a far more sophisticated actor than one might get for a role that could be looked at as just a daring, kick-ass pilot,” he says. “But I needed a great actor—not just a great-looking guy who also acts.”

Some time ago, Isaac sat down to perform a kind of exercise. “Just out of curiosity, I thought, ‘What common thread do the three last characters I played have?’ ” he says. “And yes, what they did have in common was a sense of melancholy, anger, displacement.”

Isaac's family moved to the United States from Guatemala when he was 5 months old. Back then his full name was Oscar Isaac Hernandez Estrada. The family went first to Baltimore and then to New Orleans, where his father, Oscar Gonzalo, studied to become a doctor. Finally they settled in Miami. Isaac and his siblings often accompanied their mother on trips home to Guatemala, and she spoke primarily Spanish around the house, but it was still a largely Americanized upbringing.

“It became a badge of individuality,” Isaac says. “I was the guy that didn't drink, and it just felt good to be that.”

“For my father, individualism was very important, and he instilled that in me,” Isaac says. “It was way more important to recognize myself as an individual than as part of a group. I wasn't part of the ‘Latino community.’ I was just a kid in high school with friends, who was into playing music.” He listened to the Beatles and the Cure. He played in a hardcore band and a ska-punk band called the Blinking Underdogs, writing songs about Boynton Beach trailer parks instead of London ghettos. Even within that community, he kept himself apart—going straight edge while most around him indulged in drugs and alcohol. “It became a badge of individuality,” he says. “I was the guy that didn't drink, and it just felt good to be that.” Early on, he began using his truncated and more Anglicized name, in part as a way to distinguish himself from the multitude of other Oscar Hernandezes in Miami. On the other hand, when he was 10 and his parents became American citizens and asked if he wanted to join them, he declined, not becoming a citizen until 2006.