Preheat oven to 350 degrees F. Lightly grease a 13 x 9-inch baking pan. In a large bowl, combine the cake mix, 1 egg and 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 1 stick of melted butter, and the vanilla extract, 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.