In a medium pan, combine the white sugar, brown sugar, butter, and milk. Cook on medium heat, stirring often until boiling. Boil for 1 minute and remove from heat.

Add the vanilla, peanut butter, and oatmeal. Stir until combined.

Using a soup spoon, drop onto parchment paper and let cool.

Work quickly when transferring batter to the parchment paper. As it cools, it will thicken and harden. If this happens, warm the remaining mixture in the saucepan for a couple of minutes over medium-low heat, stirring continuously. Then continue the process of placing the batter on the parchment paper.

Store in the refrigerator in an airtight container. Layer the cookies between parchment or waxed paper.