Triple Layer Chocolate Cake

Triple Layer Chocolate Cake
1 1/2 cups (3 sticks) unsalted butter, softened, plus more for the pans
2 cups granulated sugar
1 tablespoon vanilla extract
3 eggs
2 3/4 cups all-purpose flour
1 cup unsweetened cocoa
1 1/2 teaspoons baking powder
1 1/2 teaspoons baking soda
1 teaspoon salt
1 3/4 cups milk

Chocolate Butter Cream Frosting
1 1/2 cups unsweetened cocoa
5 1/2 cups powdered sugar
3/4 cup (1 1/2 sticks) unsalted butter, softened
2/3 cup (plus 1 to 2 tablespoons more, if needed) milk
2 teaspoons vanilla extract

Method
For the cake, preheat oven to 350°F. Grease and lightly flour three 8-inch round cake pans and set aside. With an electric mixer, cream together butter and sugar until light and fluffy, about 5 minutes. Add vanilla and eggs, one at a time, scraping the bowl down after each addition. In a large bowl, sift together flour, cocoa, baking powder, baking soda and salt, then add to butter mixture in batches, alternating with milk and ending with flour mixture. Do not overmix. Divide batter evenly between the three pans, smooth out and bake 25 to 35 minutes, or until a toothpick inserted in the center comes out clean. Let cakes cool slightly, then remove from pans and transfer to cooling racks to let cool completely.

Meanwhile, for the frosting, combine cocoa and powdered sugar in a medium bowl. In another bowl, use an electric mixer to cream butter with 1 cup of the cocoa-sugar mixture, then add the remaining cocoa-sugar mixture, alternating it with the milk. Beat until frosting is easily spreadable, then blend in vanilla. When cakes are completely cool, frost the top of each, then stack them evenly and frost the sides and top with remaining frosting.