Who was the first actor to direct himself in an Oscar-winning role?

Laurence Olivier.

# With this film, Laurence Olivier became the first person ever to direct themselves to a best actor or actress Oscar.

# The first film to win both the Academy Award for best picture and the Venice Film Festival Golden Lion Award for best picture.

Internet Movie Database
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http://imdb.com/title/tt0040416/awards
Hamlet (1948) won the Best Actor, Best Picture, Best Set Decoration B&W, and Best Costume Design, B&W in 1949. It was nominated for Best Actress in a Supporting Role (Jean Simmons),
Best Director (Laurence Olivier), and Best Music, Scoring of a Dramatic or Comedy Picture
(William Walton).

Good job, Mozart.