• Preheat your oven to 350 degrees Fahrenheit (175 degrees Celsius). Grease a 9-inch by 13-inch rectangular cake pan with butter and line the bottom with parchment paper. Set aside.
• In a large bowl, whisk together the sugar, flour, cocoa powder, baking soda, baking powder and salt.
• Add the milk, Baileys, vegetable oil, eggs and vanilla to a large liquid measuring cup, whisking them together with a fork.
• Whisk the wet ingredients into the dry ingredients just until the streaks of flour disappear.
• Add the boiling water or hot coffee a little bit at a time, whisking until blended.
• Pour the batter (it will be very liquid) into the prepared pan and baked at 350 degrees Fahrenheit (175 degrees Celsius) for about 30 minutes or until a toothpick inserted into the middle of the cake comes out clean.

For the frosting:

• Beat the butter on medium-high speed with a hand mixer (or in the bowl of your stand mixer fitted with the paddle attachment) until the butter is light and fluffy. Add the powdered sugar and cocoa powder and mix until blended (add the powdered sugar about 1 cup at a time).
• Add the salt and Baileys and whip on medium-high speed until incorporated.
• Add the whipping cream (start with 1 tablespoon, adding more if necessary to reach a spreadable consistency) and mix well until the frosting is fluffy and smooth.
• Spread the frosting over the cake after it has cooled completely in the pan and smooth out the top.
• Shave some dark chocolate over the top of the frosting, slice and serve.