Preheat your oven to 350°F (175°C). Grease and flour three 9-inch round cake pans.

In a large bowl, cream together the softened butter, vegetable shortening, and granulated sugar until light and fluffy.

Add egg yolks one at a time, beating well after each addition. Mix in the vanilla extract.

In a separate bowl, combine the flour and baking soda. Gradually add this dry mixture to the creamed mixture, alternating with the buttermilk. Begin and end with the flour mixture. Mix until just combined.

Fold in the shredded coconut and chopped pecans gently until evenly distributed.

In another clean bowl, beat the egg whites until stiff peaks form. Carefully fold the egg whites into the cake batter until no white streaks remain.

Divide the batter evenly among the prepared cake pans. Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cakes to cool in the pans for about 10 minutes, then transfer to wire racks to cool completely.

While the cakes are cooling, prepare the frosting. In a mixing bowl, beat the softened cream cheese and butter until smooth. Gradually add the powdered sugar and vanilla extract, mixing until creamy and spreadable.

Once the cakes are completely cool, place one layer on a serving plate. Spread a layer of frosting on top, then add the second layer and repeat. Place the third layer on top and frost the entire cake.

Garnish the top with chopped pecans and shredded coconut for an attractive finish.