Heat oven to 350 degrees. Place cake mix in a bowl. Measure 1 cup of the mix and set aside for topping. Stir melted butter and egg into remaining cake mix in bowl. Press mixture into bottom of a 9-by-13-inch cake pan.
In a separate bowl, using an electric mixer, combine pumpkin, evaporated milk, sugar, eggs, pumpkin pie spice and vanilla. Pour over cake layer in pan.
In another bowl, combine reserved cake mix, sugar and cinnamon. Using a fork or pastry cutter, cut butter into dry ingredients until crumbly. Sprinkle mixture over pumpkin filling. Bake 60 to 70 minutes. Cool.
For topping, combine pudding and milk in a bowl. Fold in whipped topping. Serve over cooled cake.