Preheat the oven to 325 degrees F. and line a 24-cup muffin tin 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 on medium-high speed until the mixture is light and fluffy.
Add the eggs and vanilla extract and beat well, 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, water and milk and whisk until combined.
In a third bowl, sift (or whisk well) the flour with baking powder and salt.
Add the flour mixture to the butter mixture, alternating with the Baileys mixture.
With the mixer on low speed, add 1/3 of the flour mixture to the butter mixture, then pour in half of the Baileys mixture. Repeat with another 1/3 of the flour mixture, followed by the remaining Baileys mixture. Finish with the remaining flour mixture. Beat on medium speed, scraping the bowl well, until the mixture is combined.
Fill cupcake liners 3/4 full and bake for 25 minutes, until a toothpick comes out clean. *Do not overbake. Allow the cupcakes to cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely before frosting.