Preheat oven to 350 degrees F. Mix butter, flour, and peanuts, and press into 9 x 13 pan. Bake for 20 minutes, or until crust is golden brown. Cool.
Beat cream cheese and powdered sugar on high speed until well blended. Mix in 1 large tub of Cool Whip. Spread over cooled crust. Mix chocolate pudding and cold milk, and spread over cream cheese mixture. Spread second large Cool Whip over the chocolate layer.