Melt 1 stick butter. Add 1 cup flour, 1/2 cup chopped nuts (walnut or pecan); mix together and press in 8x12 pan. Bake 20 minutes at 325 degrees; let cool.
Mix 1 (8 ounce) package cream cheese and 1 cup powdered sugar; add 1 cup Cool Whip to above and mix together. Spread over crust. Mix 3 cups cold milk, 1 package instant chocolate pudding (small), 1 small package instant vanilla pudding. Let set until firm, about 3 minutes. Spread over cream cheese mixture.
Cover with remaining carton of Cool Whip. Sprinkle with slivers of chocolate bar. Refrigerate until ready to serve.