CHOCOLATE LAYER CAKE WITH MILK CHOCOLATE FROSTING

Steps:

• Make cake:
• Put oven rack in middle position and preheat oven to 350°F. Butter 2 (9- by 2-inch) round cake pans and line bottom of each with a round of parchment or wax paper. Butter paper and dust pans with flour, knocking out excess.
• Sift together flour, cocoa, baking soda, and salt into a small bowl. Beat together butter and sugars in a large bowl using an electric mixer at medium-high speed until light and fluffy, 3 to 4 minutes in a standing mixer or 4 to 5 minutes with a handheld. Add eggs 1 at a time, beating well after each addition. Add chocolate and vanilla and beat until just combined. Reduce speed to low and add flour mixture and buttermilk alternately in 3 batches, beginning and ending with flour mixture and mixing until just combined.
• Divide batter between cake pans, spreading evenly, and bake until a wooden pick or skewer inserted in center of each cake layer comes out clean, 25 to 35 minutes.
• Cool cake layers in pans on racks 10 minutes. Run a thin knife around edge of each layer, then invert onto racks. Peel off paper and cool layers completely.
• Make frosting:
• Heat milk in a 1- to 1 1/2-quart heavy saucepan over moderate heat until hot. Whisk together yolks, flour, 1/3 cup confectioners sugar, and a pinch of salt in a bowl, then add hot milk in a stream, whisking. Transfer custard to saucepan and bring to a boil over moderate heat, whisking. Reduce heat and simmer, whisking, 2 minutes (mixture will be very thick), then transfer to a large bowl. Cover surface of custard with a buttered round of wax paper and cool completely, about 45 minutes.
• Add vanilla and remaining cup confectioners sugar to custard and beat with cleaned beaters at moderate speed until combined well, then increase speed to medium-high and beat in butter, 2 tablespoons at a time, until smooth. Add chocolates and beat until combined well.
• Frost cake:
• Halve each cake layer horizontally using a long serrated knife. Layer cake, using a heaping 1/2 cup frosting between each layer, then frost top and sides with remaining frosting.