Preheat oven to 350 degrees F.
Lightly grease a 13-by-9-inch baking pan. In a large bowl, combine the cake mix, 1 egg, and 8 tablespoons (1 stick) melted butter, and stir until well blended. Pat mixture into prepared pan and set aside. In a stand mixer, or with a hand mixer, beat the cream cheese until smooth. Add the remaining 2 eggs, and the cocoa powder. Lower the speed of the mixer, and add the powdered sugar. Continue beating until ingredients are well mixed. Slowly add the remaining 8 tablespoons (1 stick) of melted butter, and the vanilla, continuing to beat the mixture until smooth. Stir in nuts with a rubber spatula. Spread filling over cake mixture in pan.
Bake for 40 to 50 minutes. Be careful not to overcook the cake; the center should still be a little gooey when finished baking. Let cake partially cool on a wire rack before cutting into pieces.