Prepare two baking sheets by lining them with parchment paper or alternatively, arrange approximately 29 cupcake liners for use.

In a medium saucepan (approximately 2.5 to 3 quarts in size), combine the butter, sugar, cocoa powder, and milk. Place the saucepan over a medium heat setting.

Stir the mixture frequently and continue to cook until it reaches a full rolling boil.

Allow the mixture to boil for exactly 60 seconds, refraining from stirring during this time.

Immediately after the boiling period, remove the saucepan from the heat. Quickly incorporate the vanilla extract, peanut butter, and quick oats into the mixture, stirring until the ingredients are uniformly combined.

Using a medium-sized cookie scoop (equivalent to 2 tablespoons) or two spoons, drop the cookie mixture onto the prepared baking sheets or into the cupcake liners.

Let the cookies rest at room temperature until they are set, which typically takes about 20 to 30 minutes. For a quicker setting process, the cookies can be refrigerated.

Once set, store the cookies in an airtight container at room temperature for optimal freshness.