In a bowl, cut butter into flour; stir in the finely chopped walnuts. Press into a greased 13-in. x 9-in. baking dish. Bake at 350° for 20 minutes or until golden brown. Cool on a wire rack.
In a large bowl, beat cream cheese and sugar until smooth. Fold in 1 cup whipped topping. Spread over crust.
In another bowl, beat milk and pudding mix for 2 minutes or until thickened. Spread over cream cheese layer. Spread with the remaining whipped topping; sprinkle with coarsely chopped walnuts. Chill until set.