Beat butter and shortening at medium speed with an electric mixer until fluffy. Gradually add sugar, beating well. Add egg yolks, one at a time, beating after each addition.
Combine flour, baking soda, and cocoa; add to creamed mixture alternately with buttermilk. Stir in pecans, coconut and vanilla.
Beat egg whites at high speed until stiff peaks form; fold into batter. Pour batter into 3 greased and floured 8-inch round cakepans. Bake at 325 for 35 to 40 minutes until wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans and cool completely.
Spread Cream Cheese Frosting between layers and on top and sides of cake. Garnish with pecan halves if desired.
Cream Cheese Frosting
1 (8-ounce) package cream cheese softened
1/2 cup butter softened
1 (16-ounce) package powdered sugar
1/4 cup cocoa
1/8 tsp salt
1/2 cup chopped pecans
1 tsp vanilla extract
Beat cream cheese and butter at medium speed with an electric mixer until fluffy. Combine powdered sugar, cocoa, and salt. Gradually add to creamed mixture, beating until smooth. Stir in pecans and vanilla.