In a medium saucepan, combine the sugar, butter, milk, and cocoa powder.
Bring the mixture to a rolling boil over medium-high heat, stirring frequently.
Once at a rolling boil, boil for exactly 90 seconds.
Remove the saucepan from the heat immediately.
Stir in the peanut butter and vanilla extract until the peanut butter is fully melted and incorporated.
Add the quick-cooking oats and stir until they are thoroughly coated in the chocolate mixture.
Drop spoonfuls of the mixture onto parchment paper or wax paper.
Allow the cookies to cool and set completely at room temperature for at least 30 minutes before serving.