Prepare two cookie sheets by lining with wax paper and set aside.
Combine butter, milk, sugars, and cocoa powder in a medium-sized, heavy 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 then remove from heat.
Add peanut butter and vanilla extract, stirring until peanut butter is completely combined and melted into the mixture. I like to put back on burner on low heat to make sure mixture is hot. The cookies will have a more shiny appearance if they are really hot when you scoop them out.
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. A scoop works really good for this.
Allow to cool (approximately 20-30 minutes) before serving, the cookies will harden as they cool.