Place the butter, granulated sugar, milk, and cocoa powder in a medium saucepan. Over medium heat, bring to a boil, stirring occasionally. Once the mixture is at a rolling boil, boiling around the edges and in the middle, boil for one minute.
Remove the pan from the heat and stir in the peanut butter, vanilla, and salt. Stir until peanut butter is melted and smooth. Stir in the oats.
Drop spoonfuls of the mixture (about 2 tablespoons per cookie) onto the prepared baking sheets, and let sit at room temperature until cooled and hardened, about 20 to 30 minutes.
Store the cookies in an airtight container for up to 3 to 4 days on the counter or in the fridge.