Preheat the oven to 350 degrees F. Lightly butter a 9-by-13-inch baking pan.

In a large bowl, combine the cake mix, 1 egg and 1/2 cup of the melted butter. Stir until well blended. Pat the mixture into the pan and set it aside.

In the bowl of a stand mixer fitted with the paddle attachment, or using a hand mixer, beat the cream cheese until smooth. Add the remaining 2 eggs and the cocoa powder and beat until well mixed. Reduce the speed to low and add the confectioners' sugar. Beat until well mixed. Slowly add the remaining 1/2 cup melted butter and the vanilla. Beat until smooth. Using a rubber spatula, stir in the nuts. Spread the filling over the batter in the pan.

Bake the cake for 40 to 50 minutes. Be careful not to overcook it: The center should still be a little gooey. Let partially cool on a wire rack before slicing. Serve with whipped cream, if desired.

Photograph by Andrew Mccaul