Preheat your oven according to the instructions on the chocolate cake mix box. Prepare your baking pan by greasing it lightly.
In a large mixing bowl, combine the chocolate cake mix with the ingredients listed on the back of the box. Mix until well combined.
Pour the batter into the prepared baking pan and bake according to the package instructions, usually around 25-30 minutes or until a toothpick comes out clean.
Once baked, remove the cake from the oven and allow it to cool for about 10-15 minutes.
Using the end of a wooden spoon or a straw, poke holes all over the top of the cake.
In a medium bowl, whisk together the sweetened condensed milk, 1/4 cup of Irish cream, and 1/3 cup of heavy cream until well combined. Pour this mixture evenly over the poke holes in the cake.
In a separate bowl, whip 2 cups of heavy cream with the powdered sugar and 1/4 cup of cocoa powder until stiff peaks form. Fold in 2 tablespoons of Irish cream.
Spread the whipped topping evenly over the cooled cake, and sprinkle grated chocolate on top as a garnish if desired.
Cover the cake and refrigerate for at least 2 hours before serving.