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Preheat the oven to 350°F. Grease and flour three 8" or two 9" cake pans, and line them with parchment paper circles or reusable pan liners. Be sure your 9" pans are at least 2" deep.
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To make the chocolate stout cake: Place the stout and butter in a large, heavy saucepan, and heat until the butter melts. Remove the pan from the heat, and add the cocoa powder.
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Whisk until the mixture is smooth. Set aside to cool to room temperature.
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Whisk together the flour, sugar, baking powder, and salt in a large bowl; set aside.
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In a large mixing bowl, beat together the eggs and sour cream.
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Add the stout-cocoa mixture, mixing to combine.
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Add the flour mixture and mix together at slow speed. Scrape the sides and bottom of the bowl, and mix again for 1 minute.
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Divide the batter equally among the prepared pans. (The recipe yields about 10 cups or 2625g of batter. If you're making a double-layer cake, each pan should have about 5 cups or roughly 1312g. If you're making a triple-layer cake, each pan should have about 3 1/3 cups of batter or 875g).
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Bake the layers for 40 to 45 minutes for 8" pans, or 55 to 60 minutes for 9" pans, until a cake tester inserted into the center comes out clean. Remove the cakes from the oven and cool on a rack for 10 minutes before turning the cakes out of their pans and returning to the rack to finish cooling completely before frosting.
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To make the frosting: Place the chopped chocolate in a large heatproof bowl. Bring the cream to a simmer in a heavy, medium-sized saucepan.
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Pour the hot cream over the chocolate and stir until the mixture is completely smooth.
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Stir in the vanilla. Refrigerate until the icing is spreadable, stirring occasionally, about 2 hours.
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To assemble: Trim the top of the cake layers to be level, if necessary (otherwise the layers will crack when they are stacked).
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Line the edges of a serving plate with parchment or waxed paper to keep it clean, and then place the layer upside down on top. Spread 2/3 cup of the icing over just the top of the layer.
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Top with another cake layer, top side down, and repeat the process. If you baked three layers, add that one also.
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Use the remaining frosting to cover the top and sides of the cake. Remove the parchment or waxed paper. Sprinkle with shamrock sugar decorations, if you have them.