Fudgy Chocolate Layer Cake

1 3/4 cups all-purpose flour
1 cup less 1 tablespoon unsweetened cocoa powder
1 1/4 teaspoons baking soda
1/8 teaspoon salt
3/4 cup (1 1/2 sticks) butter, softened
2/3 cup granulated sugar
2/3 cup firmly packed brown sugar
2 large eggs
2 teaspoons vanilla extract
1 1/2 cups buttermilk

Frosting:

1/2 cup (1 stick) butter, softened
1 1/2 cup confectioner's sugar, sifted
3 ounces unsweetened chocolate, melted
2 teaspoons vanilla extract
Chocolate shavings (optional)

1. Preheat oven to 350ºF. Line bottoms of two 9-inch round cake pans with waxed paper. Grease paper and sides of pans. Dust with flour.
2. Mix flour, cocoa, baking soda, and salt. In another bowl, beat butter, granulated sugar, and brown sugar at medium speed until light and fluffy. Add eggs, 1 at a time, beating well after each addition. Add vanilla.
3. At low speed, alternately beat flour mixture and buttermilk into butter mixture just until blended. Divide batter equally between prepared pans.
4. Bake cakes until a toothpick inserted comes out clean, 25 to 30 minutes. Transfer pans to wire racks to cool for 10 minutes. Turn out onto racks. Remove paper. Turn layers topside up and cool completely.
5. To prepare frosting, beat butter and confectioner's sugar at medium speed until light and fluffy. Add melted chocolate and vanilla; continue beating until shiny and smooth. On the edges of a serving plate, place 3-4 pieces of waxed paper, folded in half.
6. Place 1 cake layer on the serving plate; spread with frosting. Top with remaining cake layer. Spread frosting on top and sides of cake. Remove waxed paper. Let cake stand for at least 30 minutes before sprinkling with chocolate shavings and slicing.