Chocolate Mayonnaise Cake
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 pan).
Bake cakes until tester inserted into center comes out clean, 30 to 32 minutes. Cool cakes in pans on rack 20 minutes. Run small knife around sides of cake to loosen. Invert cakes onto racks and cool completely.
Using electric mixer, beat butter in large bowl until smooth and creamy. Add powdered sugar 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.
Place one layer on platter. Spread 3/4 cup frosting over top of cake layer to edges. Top with second layer; spread 3/4 cup frosting over. Top with third layer. Spread remaining frosting decoratively over top and sides of cake. Cut and serve.
Do ahead: Can be made 1 day ahead. Cover with cake dome and let stand at room temperature. I think it is better if you allow to stand overnight.