Prepare and the cake mix according to package directions (add eggs, water, and oil). Pour into the prepared 9x13 pan.
Bake for 30-35 minutes and remove from the oven. Allow to cool for 10 minutes.
With a wooden spoon, poke holes in the cake evenly, about 80 holes (8 across, 10 down).
In a small bowl whisk together the pudding mix, milk and Baileys Irish Cream.
Pour pudding mixture over cake, pressing into the holes using a spatula. Place the cake in the refrigerator for at least 2 hours to let the pudding mixture set up.
To make the whipped topping, in a medium bowl beat the heavy cream. As it thickens, add the Baileys and powdered sugar until stiff peaks form.
Spread the whipped cream mixture over cooled cake and top with chocolate shavings and finely chopped pistachio nuts. [Using a cheese grater, you can grate the chocolate for the topping.]