Heat your oven to 350°F and grease a 9x13-inch baking dish.
Prepare the yellow cake batter using the ingredients and directions listed on the box.
Pour the batter into the prepared pan and bake until the cake is done. Follow the baking time recommended on your cake mix package.
Set the cake aside and let it cool completely.
Add the vanilla pudding mix and cold milk to a mixing bowl. Whisk until smooth, then let it sit for about 5 minutes so it can begin to thicken.
Take the rounded handle of a wooden spoon and poke holes all across the surface of the cooled cake.
Spoon the vanilla pudding over the cake. Spread it gently over the top, making sure plenty of pudding settles into the holes.
Cover the pan and refrigerate for several hours, giving the pudding time to soak into the cake.
When the cake is well chilled, place the chocolate frosting in the microwave for 15 seconds. Stir it, then continue warming in short 15-second bursts if needed.
Once the frosting is soft enough to spread easily, pour it over the cake.
Gently spread the frosting into an even layer.
Serve right away or refrigerate the cake again until you are ready to serve it. Keep any leftovers chilled.