To prepare cake: Preheat oven to 350 degrees. Butter and flour bottom and sides of two 10-inch cake pans. In a large bowl, sift together cake flour, baking powder and baking soda and reserve. In a bowl of an electric mixer on medium-high speed, beat granulated sugar and butter until light and fluffy, about 2 minutes, scraping down sides of bowl as necessary. Add eggs, 1 at a time, beating well after each addition. Add vanilla extract and beat until thoroughly combined. Reduce speed to low, add cocoa and mix until thoroughly combined. Add flour in three parts, alternating with coffee and ending with flour, and mix until thoroughly combined. Divide batter evenly between two prepared pans and bake until a cake tester inserted into center of cake comes out clean, about 40 minutes. Remove from oven and transfer pans to a wire rack. Cool for 15 minutes, then invert cakes onto a wire rack and cool completely.
To prepare icing: In a large saucepan over medium heat, melt butter. Add granulated sugar, stir and bring to a simmer, stirring. Remove from heat, add cream and vanilla extract and stir until smooth. Cool. Transfer mixture to a bowl of an electric mixer on low speed. Gradually add powdered sugar, beating until icing is creamy. If icing is too thick, add a little more cream, 1 teaspoon at a time.
To assemble cake: Place one cake round on a cake plate. Spread a layer of icing across top of cake. Place second cake round on top of iced round, and spread icing across top and sides of cake. Add candles, and sing "Happy Birthday."
Nutrition information per 1/16 serving: