Mix sugar, milk, and cocoa powder together in a saucepan; bring to a boil and cook at a boil for 1 minute. Remove saucepan from heat and stir peanut butter, applesauce, and vanilla extract into the hot mixture until smooth. Add oats and stir until evenly mixed.
Drop oats mixture by spoonful onto waxed paper. Cool completely before removing from paper, at least 20 minutes.