Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch springform pan.
Pour stout beer into a large saucepan over medium-low heat. Add 1 cup sliced butter; heat until butter is melted, about 5 minutes. Whisk in white sugar and cocoa powder until dissolved. Remove from heat.
Mix sour cream, eggs, and 1 tablespoon vanilla extract together in a bowl. Stir into beer mixture. Whisk flour and baking soda into the beer mixture until batter is smooth; pour into the greased pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 45 to 60 minutes. Run a knife around the edge of the cake; cool to room temperature on a wire rack, about 30 minutes. Remove ring and transfer cake to a serving platter.
Beat 1/2 cup butter and cream cheese together in a bowl. Add vanilla extract. Mix in confectioners' slowly until icing is smooth. Add Irish cream liqueur 1 tablespoon at a time to thin frosting to a spreading consistency. Spread frosting over cooled cake.
Nutritional Facts
Per 10 servings
Calories: 674
Carbohydrate: 84g
Fat: 35g
Fiber: 1g
Protein: 5g
Sugar: 67g
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