Preheat oven to 350°. Grease and lightly flour three 9 inch round baking pans.
In a large bowl, cream butter, shortening, and sugar until light and fluffy, about 5-7 minutes.
Beat in the egg yolks and vanilla extract. Combine the flour and baking soda; add to the creamed mixture alternately with buttermilk until just combined.
Fold in the coconut and pecans.
In another bowl, beat the egg whites with clean beaters until stiff. Fold the whipped egg whites into the batter. Pour into prepared pans.
Bake 20-25 minutes. Test doneness by inserting a toothpick into the middle of a cake. Allow the cake to cool for 10 minutes before removing it from pans to wire racks.
How to Make Italian Cream Cheese Frosting
For frosting, beat cream cheese and butter for five minutes until smooth. Beat in powdered sugar and vanilla for five minutes more until light and fluffy. Spread frosting between layers and over top and sides of cake.
Garnish with toasted coconut and pecans. See the tip below for how to toast shredded coconut in the oven.
Store finished cake in the refrigerator for up to one week.