Preheat the oven to 350 degrees F. and line 27 muffin tins with cupcake liners.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl with a hand mixer), cream the butter and sugar for about 4 minutes on medium-high speed, until the mixture is pale and fluffy, scraping the bowl once.
Add the eggs and egg whites, one at a time, then add the vanilla extract, beating after each addition, and scraping down the sides of the bowl with a spatula once or twice to ensure everything is fully incorporated.
In a separate bowl, combine the Baileys and milk and stir until combined.
In a third bowl, sift the flour with baking powder and salt.
With the mixer on low speed, add ⅓ of the flour mixture to the butter mixture, then pour in half of the Baileys mixture. Repeat with another ⅓ of the flour mixture, followed by the remaining Baileys mixture. Finish incorporating the ingredients by gently hand-folding with a spatula until the batter is mixed.
Fill cupcake liners ⅔ full with a #16 scoop (¼ cup), making sure not to overfill. Smooth the tops gently with the back of a spoon and tap the pan on the counter to remove any air pockets. Bake on the center rack for 18-20 minutes, until the tops spring back and a toothpick comes out clean. Allow the cupcakes to cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely before frosting.