In a medium saucepan, combine the sugar, butter, milk, and cocoa powder. Bring to a rolling boil over medium heat, stirring constantly. Let it boil for exactly one minute.
Remove the saucepan from the heat. Stir in the vanilla extract and peanut butter until well combined.
Add the quick cooking oats and stir until they are fully coated.
Drop spoonfuls of the mixture onto waxed paper. Let them cool completely before serving.
Notes
These cookies set up best when cooled at room temperature. For a firmer cookie, you can refrigerate them.