Complex sentence: Farmiga's role in Martin Scorsese's "The Departed" (2006), which won the Academy Award for Best Picture, brought her to worldwide prominence, and she was nominated for the Empire Award for Best Newcomer.
Split into simpler sentences: Farmiga's role in Martin Scorsese's "The Departed" (2006) brought her to worldwide prominence. The film won the Academy Award for Best Picture, and Farmiga was nominated for the Empire Award for Best Newcomer.