Preheat the Oven and Prepare the Pans: Preheat your oven to 350°F (175°C). Grease and flour three 9-inch round cake pans, then set them aside.

Mix the Cake Batter: In a large bowl, cream together the unsalted butter, shortening, and granulated sugar until light and fluffy. Incorporate the egg yolks individually, mixing thoroughly after each addition. Stir in the vanilla extract.

Combine Dry Ingredients and Buttermilk: In another bowl, whisk together the flour and baking soda. Gradually add the dry mixture to the butter mixture, alternating with the buttermilk, beginning and ending with the flour mixture. Stir in the flaked coconut and toasted pecans.

Beat the Egg Whites: In a separate clean bowl, whip the egg whites until they form stiff peaks. Carefully fold the whipped egg whites into the cake mixture until they are fully blended.

Bake the Cake Layers: Evenly distribute the batter among the prepared cake pans. Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean. Allow the cakes to cool in the pans for 10 minutes, then transfer them to a wire rack to cool completely.

Prepare the Cream Cheese Frosting: In a medium bowl, combine the softened cream cheese and butter, beating until you achieve a smooth and creamy texture. Mix in the vanilla extract. Gradually add the powdered sugar, continuing to beat until the frosting reaches a thick and spreadable consistency.

Assemble the Cake: Place one cake layer on a serving plate and spread a thick layer of cream cheese frosting over it. Repeat with the second layer, and then place the final cake layer on top. Apply the remaining frosting to the top and sides of the cake.

Garnish and Serve: Garnish the cake with additional chopped pecans and flaked coconut. Chill in the refrigerator for at least 30 minutes before serving to let the frosting firm up. Slice and enjoy this decadent treat!