Line a cookie sheet with wax paper or parchment paper. Set aside so you’re ready to work quickly once the mixture is done.
In a medium saucepan over medium heat, combine the sugar, butter, milk, and cocoa powder. Stir constantly until the butter is melted and the mixture is smooth.
Increase heat slightly if needed and bring the mixture to a full rolling boil. This means the entire surface is bubbling and cannot be stirred down.
Once it reaches a full rolling boil, start timing and let it boil for exactly 1 minute without stirring. This step is critical for helping the cookies set properly.
Remove the pan from heat immediately. Stir in the peanut butter, oats and vanilla until fully combined.
Drop spoonfuls onto the prepared pan using a spoon or medium cookie scoop. Let the cookies sit at room temperature until set.