Place rack in center of oven and heat to 350 degrees F. Lightly butter 2 (9-inch) round cake pans. Line with parchment paper, and dust sides with cocoa; tapping out excess. Set aside.
In a large bowl, combine 3/4 cup cocoa, the sugar, flour, baking powder, baking soda, and salt. Add butter or oil, milk, eggs, and vanilla. Using a hand-held electric mixer on medium speed, beat for 2 minutes. Add boiling water and beat to combine (batter will be thin). Divide batter evenly between prepared pans.
Bake until cake tester inserted into the center comes out clean, 30 to 35 minutes. Cool in pans for 10 minutes. Run a paring knife around edge of cakes to loosen them from pan. Invert on to a wire rack to cool completely.
Place 1 layer, top-side up, onto a serving plate. Using an offset spatula, spread with 1 cup of frosting. Top with remaining layer, bottom-side up and frost with remaining frosting.
In a medium saucepan, melt butter. Add cocoa and beat with a hand-held electric mixer to combine.
Alternately add confectioners' sugar and milk, beating on medium speed until frosting reaches a spreading consistency. Add vanilla and beat to combine. Add additional milk or sugar as needed to achieve desired consistency.
Yield: about 4 cups
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