In a medium saucepan, melt the butter over medium heat.
Add the granulated sugar.
Stir in the cocoa powder until well combined.
Pour in the milk and stir until the mixture is smooth.
Bring the mixture to a gentle boil and cook for 1 minute, stirring occasionally.
Remove the saucepan from the heat. Add the peanut butter and vanilla extract, then stir until smooth and fully combined.
Add the quick-cooking oats.
Stir until all the oats are evenly coated with the chocolate mixture.
Using a cookie scoop or tablespoon, drop spoonfuls of the mixture onto a parchment-lined baking sheet or tray.
Gently shape the cookies if needed.
Let the cookies cool at room temperature for 20–30 minutes, or until firm and set.
Serve immediately or store the cookies in an airtight container for up to 1 week.