Cover two cookie sheets with wax paper.
Combine the sugar, cocoa, milk, and butter in a large saucepan. Stir occasionally while bringing to a boil. Boil for one minute.
Add the oatmeal, peanut butter, and vanilla. Stir until just combined. Turn off the heat.
Using a spoon, drop the mixture in tablespoon-sized portions onto the wax paper-covered cookie sheets. There should be just enough room to fit all of the cookies onto two cookie sheets.
Put the cookies into the refrigerator to cool. Once the cookies have cooled, you can store them in the refrigerator or in a sealed Tupperware container at room temperature.