Grease a 9x13-inch baking dish. Heat the oven to 350°F, unless the cake-mix package gives a different temperature for your pan.
Prepare the yellow cake batter with the ingredients and directions on its package. Pour into the prepared dish and spread evenly. Bake for the package’s recommended time, until a toothpick inserted in the center comes out without wet batter. The 30-minute cook time is an estimate.
Leave the cake in the baking dish and let it cool completely before filling. Allow about 1 hour for planning; the time can vary.
Use the rounded handle of a wooden spoon to make holes roughly 1 inch apart across the cooled cake. Press well into the sponge without pushing against the bottom of the dish. Make the holes before whisking the pudding.
Whisk the two small boxes of vanilla instant pudding mix with 4 cups of cold milk, following the package’s mixing directions. Let it begin to thicken, but use it while it is still pourable rather than waiting until it fully sets.
Spoon the pudding over the cake, gently guiding it into the holes. Spread the remainder across the surface. Cover and refrigerate for at least 3 hours, or until the pudding is set and the cake is thoroughly chilled.
Transfer the chocolate frosting to a microwave-safe bowl. Warm for 15 seconds and stir, repeating in short 15-second bursts only until it spreads easily. It should not be hot. Gently spread over the chilled pudding with light spatula strokes.
Cut into 12 pieces, wiping the knife between cuts. Lift each square with a spatula. Serve chilled, or refrigerate briefly after frosting if you want the topping a little firmer.