Combine the chocolate pudding mix and the milk in a small saucepan. Cook over medium heat, stirring constantly, until it thickens and bubbles are just beginning to form.
Remove from the heat and pour the pudding into a large mixing bowl. Press wax paper against the surface of the pudding and cool to room temperature.
Preheat oven to 350 degrees F. Grease a 9x13-inch baking pan.
Remove the wax paper from the pudding and give it a stir. Add the chocolate cake mix to the bowl and stir to combine, ensuring there are no pockets of dry ingredients. Pour the batter into the prepared baking pan and smooth into an even layer. Sprinkle the top with the chocolate chips and walnuts.
Bake for 30 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool completely before serving. Leftovers can be stored in an airtight container or covered tightly with plastic wrap at room temperature for up to 3 days.