Melt butter in a large saucepan over medium heat; add sugar, milk, and cocoa powder. Bring mixture to a boil, about 5 minutes; stir in peanut butter until melted, about 5 minutes. Return mixture to a boil and turn heat to low; simmer, stirring constantly, for 2 minutes. Remove saucepan from heat; stir in vanilla extract.
Fold oats into mixture until thoroughly mixed. Drop mixture by spoonfuls onto a sheet of waxed paper; cool to room temperature.