"I don't know how fast these things go," says Aaron Paul, clutching a black-and-white-striped racing helmet, assertively flipping up the Plexiglas face shield. "I hope they go fast. Oh, yeah. I bet we can get these things going." Paul earnestly sizes up his ride: the freshly detailed No. 14 go-kart on the track at Karting Almería in Andalucía, Spain. It's not exactly the souped-up Mustang he throttles cross-country in next month's street-racing revenge drama Need for Speed, but Paul nevertheless looks pumped. "Are the laps timed?" he asks the course keeper. Si. "Great," says Paul, his sky-blue eyes widening. "I like that. I like to see the progress. I like to see if I can beat my best effort."

That might be easier said than done for Paul. For someone who spent five seasons on Breaking Bad, playing Jesse Pinkman—a huggable murderer, a heartbreaking and heartbroken addict, the ever-manipulated pawn of a master's mastermind who grappled for 62 episodes to get a handle on his own free will, all while spouting pithy memes (Yeah, bitch; Yeah, science; Yeah, bitch. Magnets!; Yo!) and heavy, haunting tears—progress, career-wise, is hard to measure. As a character, Jesse evolved, moving along a continuum that ranged from shiftless screw-up to morally complex mensch. He entered the picture as a wigga naïf, dressed like an extra in an Insane Clown Posse video, cooking product laced with chili pepper. He left scarred and bruised, having been tested like Job.

It was the kind of role, on the kind of show, that could retool the conventional Hollywood star machine, one that makes a case for television as the superior character-minting medium of our time, and one that also sends Paul into movies as something more than just a hungry call-up from the minor leagues. At 34, he is a four-time Emmy nominee and a two-time winner who's a virtual lock for a third statue later this year. But the transition from premium-cable royalty to bona fide big-screen stud is hardly a given. Still, Breaking Bad's creator, Vince Gilligan, views Paul's ascension as an inevitability. "Aaron is going to be one of the all-time greats," he says. "Forty years from now he'll be picking up his lifetime-achievement award at the Oscars."

Before Paul can reach the promised land Gilligan foresees, he must wander in the desert. For 40 years. He is here in Almería filming Ridley Scott's 2014 holiday tentpole, the biblical epic Exodus. Paul plays Joshua, the Hebrew slave turned military savant who helps Christian Bale's Moses lead the Jews to their geographical and spiritual destiny. "This Joshua is just ready to fight," Paul says. He has been filming for a month now, working with the famously intense Bale (Paul calls him "funny," then "hilarious") and the demanding Scott ("the greatest guy") while living with his 26-year-old wife, Lauren, in a walk-up flat on a narrow Renaissance-era street. Inside, jasmine-scented candles burn low and a Bose speaker plays the ongoing indie-folk love theme of the Pauls' perpetual honeymoon. They married last May and have just returned from Paris a few hours ago, after a quick jaunt to revisit the site of their engagement and to see their friends the Lumineers perform. Still, they've already set their long wooden table with wine, cheese, crushed tomatoes, olives, crusty bread, and petals of ibérico ham arranged in concentric circles on a plate.

The Pauls met at Coachella in 2010, became friends, and, a year later, coupled up at the same festival. "Not on drugs," says Paul, a hopeless romantic dressed entirely in black. "The only people not on drugs," says Lauren. Arcade Fire belted out their anthemic finale. A mass of white balloons floated into the starry desert sky. "Normally, I drink a lot at those festivals," Paul says. "But we were just so distracted with the high that was happening between us. It's unexplainable. I told her that night I was going to marry her. I did. I told her that. I knew what she was all about. I mean, come on, she runs an antibullying nonprofit called Kind Campaign." They had their first kiss on a Ferris wheel, and their first official post-Coachella date involved flying to Vegas and driving the 1965 Shelby Cobra Paul bought on eBay back to Los Angeles, top down.