Preheat the oven to 350 degrees F (175 degrees C). Line a muffin tin with paper liners.
Combine stout beer and butter in a large saucepan over low heat. Heat until butter melts, about 5 minutes. Remove from heat and whisk in brown sugar and cocoa.
Whisk sour cream, eggs, and vanilla extract in a bowl; pour into the saucepan and mix until a smooth batter forms.
Stir flour and baking soda together. Fold into the batter. Divide batter evenly among the prepared muffin cups.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 25 minutes. Leave in the tin for 10 minutes, then transfer to a wire rack to cool completely.
Make frosting while the cupcakes cool. Place butter in a large mixing bowl and beat with an electric mixer on medium-high speed for 2 to 3 minutes. Mix in Irish cream and whiskey on low speed. Gradually spoon in confectioners’ sugar, mixing on low speed until frosting is smooth and creamy.
Spread frosting over cupcakes.
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