In a 3-quart medium saucepan combine butter, sugar, cocoa and milk. Set over medium heat and cook, stirring frequently, until it reaches a full boil. Allow mixture to boil 60 seconds without stirring.
Remove from heat, immediately add in vanilla, peanut butter and quick oats. Do not use old fashioned oats. Stir mixture until well combined and then, using a medium cookie scoop or two spoons, drop mixture onto lined baking sheets.
Allow to rest at room temperature until set, about 20 to 30 minutes. Store cookies in an airtight container at room temperature.