Line two baking sheets with parchment paper and set aside.
In a medium saucepan combine 2 cups sugar, ½ cup milk, 1 stick (½ cup) butter, and ¼ cup cocoa powder.
Place the saucepan over medium heat and stir occasionally until the mixture reaches a full, rolling boil.
Once at a full, rolling boil, continue boiling and stir constantly for 1 full minute, then remove the pan from the heat.
Immediately add 3 cups quick oats (NOT old fashioned), 1 cup smooth peanut butter, and 1 tablespoon vanilla. Stir until the mixture is uniformly combined.
Using a tablespoon measure or a medium cookie scoop (about 1 tablespoon), drop rounded tablespoons of the mixture onto the prepared baking sheets, spacing them about 1–2 inches apart. Work quickly, as the mixture will begin to set as it cools.
Let the cookies cool at room temperature on the baking sheets until firm and set (about 20–30 minutes), then serve.