Begin by preparing your batter in a large mixing bowl. Beat together 1/2 cup softened butter, 1/2 cup vegetable oil, and 1 3/4 cups sugar until the mixture is smooth and well combined. Add 2 eggs one at a time, beating thoroughly after each addition to guarantee proper incorporation.
Stir in 1 teaspoon vanilla extract. In a separate bowl, combine the dry ingredients: 2 1/4 cups flour, 1/4 cup baking cocoa, 1 teaspoon baking soda, 1/2 teaspoon baking powder, 1/2 teaspoon ground cinnamon, and 1/2 teaspoon ground cloves.
Add this dry mixture to the batter alternately with 1/2 cup buttermilk, beginning and ending with the dry ingredients. This alternating method helps create a smooth, lump-free batter. Gently fold in 2 cups shredded zucchini and 1 cup flaked coconut until evenly distributed throughout the batter.
Pour the batter into a greased 13 x 9 x 2 inch baking pan and bake at 325°F for 45-50 minutes, or until a toothpick inserted near the center comes out clean. While the cake bakes, prepare the frosting by combining 6 tablespoons softened butter, 2/3 cup packed brown sugar, 1/2 cup chopped walnuts, and 1/4 cup milk in a bowl. Once the cake is done baking, remove it from the oven and allow it to cool on a wire rack for 10 minutes.
Spread the frosting mixture over the warm cake while it's still in the baking pan. Place the pan under the broiler 4-6 inches from the heat and broil for 2-3 minutes, watching carefully, until the frosting turns golden brown. Remove from the broiler and allow the cake to cool completely before serving.
