Preheat the oven to 325°F and grease and flour 3 (9-inch) cake pans.

In the bowl of an electric mixer fitted with a paddle attachment, cream the shortening, 1 stick of the butter, and the granulated sugar until light and fluffy. Add the egg yolks one at a time, beating well after each addition. Sift the flour, baking soda, and salt together onto a sheet of waxed paper or parchment paper. With the mixer on low speed, add the sifted ingredients in batches alternately with the buttermilk, beginning and ending with the dry ingredients.

In a separate bowl, beat the egg whites until stiff. Gently fold into the batter. Add the coconut, pecans, and vanilla and fold into the batter. Divide the batter evenly among the 3 prepared cake pans and bake until cakes are golden brown and a tester comes out clean, 25 to 30 minutes. Allow the cakes to cool in the pans for 10 minutes, then turn them out onto wire racks to finish cooling. When the cakes are completely cool, stack the layers with the frosting and frost the sides and top. Decorate with additional coconut and chopped pecans if desired.

While the cakes are baking, prepare the frosting. In a large bowl combine the cream cheese with the remaining stick of butter, remaining vanilla extract, coconut extract, and coconut milk. Using an electric mixer, beat until smooth and creamy. Add the powdered sugar and mix until thoroughly combined. Keep refrigerated until you are ready to frost the cake.