Preheat oven to 350 degrees. Line 24 muffin cups with paper liners.
Cupcakes: In a medium saucepan, bring stout and 1 cup butter to a simmer. When butter has melted, remove from heat and whisk in cocoa powder until smooth; set aside to cool.
In a large bowl, combine the flour, granulated sugar, baking soda, and salt. Whisk the dry ingredients until well combined; set aside.
In a large bowl, beat the eggs and sour cream together with an electric mixer on low until well combined. Slowly beat in the cocoa mixture, then the flour mixture; beat until the batter is smooth.
Divide batter between the prepared cupcake cups, filling each cup about 2/3 full. Bake in preheated oven for 16 to 19 minutes, until a toothpick inserted into the center of a cupcake comes out clean. Cool the cupcakes completely. Spread or pipe frosting on cooled cupcakes.
Frosting: In a large mixing bowl, with an electric mixer, beat the butter until light and fluffy. Slowly add confectioners' sugar and 3 tablespoons of the Irish cream. Beat on medium speed, adding more Irish cream (a tablespoon at a time) until the frosting reaches a good consistency for frosting or piping.