Two men to date have won Oscars for Best Picture (awarded, of course, to the producer) and Best Actor, but only one of them won both for the same film. Laurence Olivier's multitasking abilities had already been recognized by the Academy in 1946, when they took the relatively unusual step of handing him an Honorary Oscar for his achievement in directing, producing and acting in his bold Shakespeare adaptation "Henry V," for which he also received Best Picture and Actor nominations. Two years later, he won both those awards for another rendition of a Bard classic, "Hamlet," making it the first non-US film to claim the Academy's top prize. He lost Best Director to John Huston or "The Treasure of the Sierra Madre," and would never receive another non-acting nomination -- though he'd end his career with 10 performance citations. 

Wins: 
"Hamlet" (1948) - Best Picture, Best Actor