Preheat oven to 400 F. Prepare your mini cupcake tin with liners.
Cream together the sugar and butter until light and fluffy in a stand mixer with a whisk attachment. Beat in the eggs one at a time.
In a separate bowl, mix together the dry ingredients then slowly add to the stand mixer going on low speed. Pause every 1/4 cup or so to let the dry ingredients to become fully incorporated.
Once the cupcake batter has reached a thick, yet creamy state, slowly pour in the 1/2 cup of Bailey's Irish cream 1 tablespoon at a time until the battery is smooth, but not runny.
Fill each cupcake liner with about a tablespoon of batter, or about 2/3 full. Pop into the oven for 20-25 minutes. Be sure to test with a toothpick and only remove from the oven when the toothpick comes out clean of the center of the middle muffin.
Allow to cool for about 10 minutes in the pan before flipping onto a cooling rack to cool completely.
In a small bowl or plate, pour 1/4 of the Bailey's Irish Cream, then dunk each cupcake into the Bailey's for about 30 seconds to absorb as much alcohol as possible. Seal in a container until ready to decorate with icing.
Using a large stand mixer with a whisk attachment, combine the room temperature butter with the powdered sugar, one tablespoon at a time. Slowly add the Bailey's Irish Cream until the frosting is thick, alternating with the powdered sugar to reach the desired consistency.
Add the food coloring and whisk on high speed until light and fluffy. Spoon into a icing bag with your favorite tip.
Once the cupcakes are completely cooled, start the icing in the middle of the cupcake and twirl outwards and upwards! Chill or serve right away at room temperature. Store leftover cupcakes in an airtight container in the fridge for up to 3 days.