Chocolate Stout Layer Cake with Chocolate Frosting

Position rack in center of oven and preheat to 350°F. Butter and flour two 9-inch-diameter cake pans with 1 1/2-inch-high sides. Line bottom of each cake pan with parchment paper round; butter and flour parchment. Place chopped chocolate in medium metal bowl. Set bowl over saucepan of barely simmering water and stir until chocolate is melted and smooth. Remove bowl from over water and set aside.

Whisk flour, baking powder, baking soda, and salt in medium bowl to blend. Using electric mixer, beat butter and 11/4 cups sugar in large bowl until fluffy and pale yellow, about 2 minutes. Add egg yolks 1 at a time, beating until well blended after each addition. Beat in lukewarm melted chocolate, then stout and coffee. Beat flour mixture into chocolate mixture in 2 additions just until incorporated.

Using clean dry beaters, beat egg whites and remaining 3 tablespoons sugar in another medium bowl until stiff but not dry. Fold 1/3 of egg whites into cake batter to lighten, then fold in remaining egg whites in 2 additions. Divide batter between prepared cake pans (about 3 cups for each); smooth tops.

Bake cakes until tester inserted into centers comes out clean, about 30 minutes. Transfer cakes to racks and cool in pans 20 minutes. Invert cakes onto racks; remove parchment paper and cool completely. DO AHEAD: Can be made 1 day ahead. Cover and store at room temperature.

Place chopped chocolate in medium heatproof bowl. Combine whipping cream and espresso powder in medium saucepan. Bring cream mixture to simmer over medium-high heat, whisking occasionally. Pour cream mixture over chopped chocolate; let stand 1 minute, then whisk until chocolate is melted and mixture is smooth. Chill chocolate frosting until slightly thickened and spreadable, stirring occasionally, about 2 hours (or for quick chilling, place frosting in freezer until thickened and spreadable, stirring occasionally, about 30 minutes).

Using serrated knife, trim rounded tops from both cake layers so that tops are flat. Place 1 cake layer, trimmed side up, on 9-inch-diameter tart pan bottom or cardboard round, then place on rack set over baking sheet. Drop 1 1/4 cups frosting by large spoonfuls over top of cake layer; spread frosting evenly to edges with offset spatula or butter knife. Top with second cake layer, trimmed side down. Spread remaining frosting evenly over top and sides of cake. DO AHEAD: Can be made up to 1 day ahead. Cover with cake dome and refrigerate. Let cake stand at room temperature at least 1 hour and up to 3 hours before serving.