Preheat oven to 350 degrees F (175 degrees C) and lightly grease a 9x13 inch baking dish.
Set aside 1 cup of cake mix. Combine remaining cake mix with melted butter and 1 egg and mix until well blended; spread mixture in the bottom of the prepared baking dish.
In a large bowl combine pumpkin, brown sugar, milk, 3 eggs and pumpkin pie spice; mix well and pour this mixture over cake mix mixture in baking dish.
In a small bowl with a pastry blender, or in a food processor, combine chilled butter and white sugar with reserved cake mix until mixture resembles coarse crumbs. Sprinkle over pumpkin mixture. Sprinkle chopped walnuts over all.