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For the cake:
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Preheat oven to 350 F. Grease three 9-inch cake pans and set aside.
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In a large bowl, sift the flour, baking powder, baking soda and salt. Set aside.
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Beat butter and sugar together on medium speed in the bowl of a standing mixer until light and fluffy. Beat in vanilla, then eggs, one at a time, until blended.
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Reduce the speed to low and beat in buttermilk, until just combined. Then add flour mixture in three batches, mixing until each addition is just incorporated before adding the next.
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Pour the mixture into the prepared cake pans and spread evenly.
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Bake for 25 to 30 minutes or until a wooden pick inserted into the cake comes out clean. Cool in pans on a wire rack for about 10 minutes before inverting the cakes out of the pans onto the rack. Let them cool completely.
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To prepare buttercream, put butter into a medium-sized bowl and beat on high speed until fluffy. Add melted chocolate and sugar and beat until incorporated.
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Add cream and beat until you get to the right spreading consistency.
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To assemble the cake, place one cake layer on your serving plate and spread with 1/3 cup of the chocolate buttercream. Place another cake layer on top, and gently press down a little bit. Spread with another 1/3 cup of the buttercream. Place the final cake layer on top. Smear the remaining buttercream on the top and sides of the cake.
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To decorate, use an offset spatula to gently smear vertical lines from the bottom against the sides of the cake. Garnish with some raspberries.
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Recipe adapted from SmittenKitchen's Best Birthday Cake recipe.