Grease and lightly flour two 9x1-1/2-inch round baking pans; set pans aside.
Stir together the flour, cocoa powder, baking powder, and baking soda.
In large mixing bowl, beat butter with electric mixer on medium speed for 30 seconds.
Add sugar, oil, and vanilla; beat until well combined. Add eggs, one at a time, beating 1 minute after each addition. Add the sour cream; beat until combined.
Add the dry ingredients to beaten mixture, beating on low speed until just combined. Fold in the zucchini. Divide batter between the prepared pans.
Bake in a 350 degree F oven for 35 to 40 minutes or until a toothpick inserted near the center of each cake comes out clean.
Place cakes on wire racks; cool in pans for 10 minutes. Remove cakes from pans and cool thoroughly.
To frost, place one cake layer on a cake plate. Spread with some of the Chocolate Butter Frosting. Sprinkle frosting with half of the chocolate pieces and nuts. Place second layer on top. Frost top and sides with remaining frosting. Sprinkle top and sides with remaining chocolate and nuts. Makes 12 servings.
In a bowl, beat cocoa powder and butter with an electric mixer on medium speed until fluffy. Gradually add 2 cups sifted powdered sugar, beating well. Slowly beat in milk and vanilla. Slowly beat in 2 cups sifted powdered sugar. Beat in additional milk, if needed, to make a spreading consistency.