Prepare two cookie sheets by lining with wax paper and set aside.
Combine butter, milk, sugars, and cocoa powder in a medium-sized saucepan over low heat. Don't bump up the heat to speed up the process or you run the risk of your ingredients not combining properly and your cookies not setting properly.
Stir ingredients frequently until butter is completely melted (I recommend using a long wooden spoon as a metal spoon can become really hot).
Increase heat to medium and, stirring constantly, bring to a boil.
Boil, still stirring constantly, for 1 minute (I recommend using a timer, see post for more details on why it's important to not over or under-boil) then remove from heat. Continue to stir the mixture for several seconds.
Add peanut butter and vanilla extract, stirring until peanut butter is completely combined and melted into the mixture.
Add oats and stir until coated in chocolate.
Drop no bake cookie mixture by approximately 1 ½-2 Tablespoon-sized spoonfuls onto prepared cookie sheet.
Allow to cool (approximately 20-30 minutes) before serving, the cookies will harden as they cool.
¹I have only ever made these cookies using whole milk and that is what I recommend. However, readers have reported success using 2% milk, skim milk, evaporated milk, and almond milk.²I do not recommend using a natural peanut butter (the kind where the oil separates).³You may substitute old-fashioned oats but the cookies will have a different texture. Please see my post for more information.