Line two baking sheets with parchment and set aside.
Combine butter, sugar, milk, and cocoa in a medium saucepan over medium heat, stirring until melted.
Bring to a steady boil and cook for 1 minute without stirring. Remove from heat.
Stir in peanut butter, vanilla, and salt until the mixture is silky and smooth.
Fold in oats until evenly coated and thick.
Scoop heaping tablespoons onto the lined sheets and gently flatten the tops.
Let cookies set at room temperature 20–30 minutes, or chill 10 minutes to speed it up.