Step 1

Preheat oven to 350°F. Butter and flour three 8-inch-diameter cake pans with 1 1/2-inch-high sides. Combine chopped chocolate and cocoa powder in medium metal bowl. Add 1 3/4 cups boiling water and whisk until chocolate is melted and mixture is smooth.

Step 2

Sift flour, baking soda, and baking powder into another medium bowl.Using electric mixer, beat both sugars and mayonnaise in large bowl until well blended, 2 to 3 minutes. Add eggs 1 at a time, beating until well blended after each addition. Beat in vanilla. Add flour mixture in 4 additions alternately with chocolate mixture in 3 additions, beating until blended after each addition and occasionally scraping down sides of bowl. Divide batter among prepared cake pans (about 2 1/3 cups for each).

Step 3

Bake cakes until tester inserted into center comes out clean, 30 to 32 minutes. Cool cakes in pans on racks 20 minutes. Run small knife around sides of cakes to loosen. Carefully invert cakes onto racks and let cool completely.

Step 4

Place chopped chocolate in medium metal bowl; set bowl over saucepan of simmering water and stir until chocolate is melted and smooth. Carefully remove bowl from over water; let melted chocolate cool until lukewarm, stirring occasionally.

Step 5

Using electric mixer, beat butter in large bowl until smooth and creamy. Sift powdered sugar over butter and beat until well blended, about 2 minutes. Beat in vanilla. Add melted chocolate and beat until well blended and smooth, occasionally scraping down sides of bowl.

Step 6

Place 1 cake layer on platter. Spread 3/4 cup frosting over top of cake layer to edges. Top with second cake layer; spread 3/4 cup frosting over. Top with third cake layer. Spread remaining frosting decoratively over top and sides of cake. DO AHEAD: Can be made 1 day ahead. Cover with cake dome and let stand at room temperature.

Step 7

Cut cake into wedges and serve.