Preheat oven to 350 degrees with a rack in the upper and lower thirds. Fill two 12-cup cupcake pans with paper liners.
In a saucepan, heat the butter, stout, cocoa powder, and brown sugar, whisking often, until the butter is melted and mixture is smooth. Remove from heat and cool to room temperature.
Into the bowl of a stand mixer fitted with the paddle attachment, combine flour, granulated sugar, baking soda, and salt.
Add cooled Guinness mixture and beat on medium for 1 minute.
Add eggs and sour cream and beat on medium for 2 minutes, scraping down the bowl as necessary, until smooth.
Divide batter evenly among cupcake liners, filling about ⅔ full. Transfer to oven and bake 20-25 minutes, rotating halfway through, until a toothpick inserted into the center of a cake comes out clean.
Cool in pan 10 minutes, then remove and transfer to a cooling rack until completely cooled.
Meanwhile, in bowl of stand mixer fitted with the paddle attachment, cream butter until light and fluffy.
Add salt, and slowly add confectioners sugar.
Add 6 tablespoons Irish Cream and milk, adding more milk as necessary, until spreadable consistency is achieved.
Transfer to a piping bag or ziplock fitted with a star tip and wash stand mixer bowl.
In bowl of stand mixer fitted with the whisk attachment, whip cream until stiff peaks form.
Add remaining 2 tablespoons Irish cream and a pinch of salt and whisk to combine.
Transfer to a pastry bag fitted with a ½-inch pastry tip.
Insert tip into tops of cupcakes and divide whipped cream mixture evenly among cupcakes, dispensing approximately 1 tablespoon per cupcake.
Frost tops of cupcakes with Bailey's frosting and sprinkle with green sprinkles. Serve.