Line a large baking sheet with parchment paper.
Add the butter, sugar, milk, cocoa powder, and salt to a medium heavy-bottomed saucepan.
Cook over medium heat, stirring occasionally, until the butter melts and the mixture comes together.
Bring the mixture to a full rolling boil.
Once it reaches a full boil, stir continuously and boil for exactly 60 seconds.
Remove the saucepan from the heat immediately after the 60 seconds are complete.
Stir in the peanut butter and vanilla until smooth.
Add the quick-cooking oats.
Stir until all the oats are evenly coated and the mixture becomes thick.
Drop rounded tablespoons of the mixture onto the prepared parchment.
Gently flatten the tops if desired.
Let the cookies sit at room temperature for about 20–30 minutes, or until firm.