Preheat Oven and Prepare the Cake Pans - Preheat the oven to 325 degrees Farenheit. Grease all three of the 8-inch round cake pans with cooking spray.
Separate the Eggs - Carefully separate the egg yolks and egg white into two small balls.
Cream Butter, Shortening, and Sugar - Using an electric mixer, cream the butter, shortening, and sugar. Once combined, mix in the egg yolks one at a time, beating well after every addition. Next, add in the vanilla extract.
Sift the Dry Ingredients - Using a sifter, sift together the flour, baking soda, and cocoa powder.
Combine Dry Ingredients With Wet Ingredients - Alternate adding the dry ingredients of the cake and buttermilk to the wet ingredients of the cake. Begin and end with the dry ingredients, mixing until combined. Stir in the chopped pecans and coconut.
Beat the Egg Whites - Using your electric mixer, beat the egg whites for a few minutes until stiff peaks form. Gently fold the egg whites with stiff peaks into the cake batter.
Bake the Cake - Pour the batter into the three-round prepared cake pans. Bake the chocolate Italian cakes for 25-30 minutes, or until a toothpick inserted into the middle comes out clean. Cool the cakes on a wire rack.
Make the Frosting - Using your large bowl with an electric mixer, beat the cream cheese and butter together until the two become smooth. Sift in the powdered sugar and cocoa powder, adding just a bit at a time. Mix in one teaspoon of vanilla and chopped pecans.
Decorate Cake - Spread a layer of frosting between each cake layer then frost the top and sides of the cake. If desired, top with additional pecans and coconut. Slice and serve the cake.