Preheat the oven to 325 degrees F and grease and flour 3 (9-inch) cake pans.
In the bowl of an electric mixer cream the shortening, butter and sugar until light and fluffy. Add the egg yolks 1 at a time, beating well after each addition. Sift the flour and salt together onto a sheet of waxed or parchment paper. In a separate bowl, mix the buttermilk and baking soda together. With the mixer on low speed, add the sifted ingredients in batches alternately with the buttermilk mixture, beginning and ending with the dry ingredients.
In a separate bowl, beat the egg whites until stiff, and gently fold into the prepared batter. Add the vanilla. Divide the batter among the 3 prepared cake pans and bake for about 25 minutes, or until golden brown and a tester comes out clean when inserted into the middle of each cake. Allow the cakes to cool in the pans for about 10 minutes before turning them out onto a wire rack to finish cooling. When the cakes are completely cool, stack the layers with the frosting and frost the sides and top.
While the cake is baking, prepare the frosting. In a large bowl combine the cream cheese, butter, vanilla and sour cream, and, using an electric mixer, beat until smooth and creamy. Add the sifted powdered sugar and mix until thoroughly combined. Keep refrigerated until you are ready to frost the cake.