Preheat the oven to 350. In a large bowl using an electric mixer beat, together the eggs, milk, butter, and Bailey's for the cake. When the wet ingredients are combined, slowly pour in the dry ingredients and mix until incorporated, pouring into two greased 8 inch round pans. Bake cakes until set for approximately 24-27 minutes or until a toothpick inserted in the middle comes out clean. When cake is done, let cool. Then remove from pan prior to frosting.
To make the frosting, sift together the cocoa powder and the confectioners sugar into a large bowl. Add the butter and mix with an electric mixer until incorporated. Add the boiling water and Bailey's and beat until smooth.
To assemble the cake, place one layer on a cake dish. Frost the cake by spreading the frosting evenly over the top of the cake and down the sides. Place the second layer on top of the first and frost the top, spreading it down the sides, using frosting to cover any gap between layers. Slice and enjoy.
Notes
If you don't love a heavily frosted cake, you may have frosting left over.