Heat oven to 350 F.
Whisk together flour, cocoa powder, baking powder, baking soda and salt.
In a stand mixer, combine butter and 1 cup of sugar; beat until soft and fluffy.
Add the whole egg, yolk and vanilla; beat until combined.
With mixer on low speed, slowly add in flour mixture, milk and espresso, alternating ¼ cup at a time until gone.
Line a muffin tin with cupcake liners. Fill each liner ⅔ full with cupcake batter and bake for 15-20 minutes.
In a stand mixer, beat together butter, Baileys, milk and vanilla until smooth.
With the mixer on low speed, mix in confectioners sugar ½ cup at a time until desired consistency is reached.
Remove cupcakes from muffin tin; spread frosting evenly on top.