Preheat your oven to 350 degrees. Grease and flour 3 9-inch cake pans, or spray with Baker’s Joy baking spray (nonstick spray that already has flour in it).
Cream the butter and shortening with an electric mixer. Add sugar and beat until smooth. Mix in egg yolks.
In a separate bowl, whisk together the flour, baking soda, and salt. Add the flour mixture to the butter mixture, alternating with the buttermilk.
Stir in the vanilla extract, coconut, and pecans. Fold in the egg white.
Pour batter into prepared pans. Bake for 22-25 minutes. Remove from the oven and let cool.
Cream together the cream cheese and butter. Beat in the powdered sugar 1 cup at a time until all is incorporated and smooth. Mix in the vanilla extract and fold in the pecans. If the frosting is too thick for your liking, add a splash or two of milk to thin it down a little.
Spread some frosting on top of the bottom layer of cake. Top with the second layer and cover with frosting. Top with the third layer of cake and spread the remaining frosting on the top and the sides. Store in the refrigerator.