Melt butter slowly over medium heat. Combine sugar and milk. Add to melted butter and blend completely with whisk. Bring to a rolling boil, and let boil 1 minute only.
Remove from heat. Add vanilla and peanut butter. Stir until smooth. Add oats and mix thoroughly. Drop from teaspoon onto waxed paper and let set until firm. NOTE: old fashioned oats will make a chewier cookie.