Preheat the oven to 350°F. Line the cupcake pans with paper liners.
In a large mixing bowl, sift together the flour, sugar, baking powder, salt, and cocoa powder.
Make a well in the flour mixture and add the mayonnaise, water, Bailey's Irish Cream and vanilla. Mix with hand mixer on medium speed for 2 minutes, or until smooth.
Using a ¼ cup measure, scoop batter into the cupcake liners. Bake for approximately 20 minutes or until no longer wet on top and toothpick comes out clean. Transfer cupcakes to a wire rack and cool completely.
FOR THE FROSTING
In a medium sized mixing bowl, blend together the cream cheese, butter, and Bailey's Irish Cream.
Gradually add the powdered sugar, to the cream cheese mixture, mixing well until well combined. Add more cream if needed to obtain spreading consistency.
This frosting will harden in the fridge, so plan to frost your cupcakes as soon as you are done making the frosting, If refrigerated, you will need to bring back to room temperature prior to frosting.