Before you begin, gather and measure all of your ingredients. Line two large baking sheets with parchment paper and set them aside.
In a large saucepan, combine the butter, sugar, milk, and unsweetened cocoa powder. Place the pan over medium heat. Stir often as the butter melts and everything blends together smoothly.
Once the mixture comes to a full rolling boil, set a timer and let it boil for exactly 60 seconds. Stir occasionally while it boils.
Remove the saucepan from the heat. Stir in the peanut butter and vanilla extract until smooth and fully combined. Add the quick-cooking oats and stir until all the oats are evenly coated and mixed in well.
Drop spoonfuls of the mixture onto the prepared baking sheets. You can use a spoon or a 1.5 tablespoon cookie scoop for even portions.
Let the cookies cool for 20 to 30 minutes, or until set. Then serve and enjoy.