1. Preheat the oven to 350°F and grease and flour three 9-inch round cake pans.
2. In a large mixing bowl, cream together the butter, oil, and granulated sugar until light and fluffy.
3. Add the egg yolks one at a time, beating well after each addition.
4. In a separate bowl, combine the flour and baking soda.
5. Add the flour mixture to the creamed mixture, alternating with buttermilk and vanilla extract.
6. In another bowl, beat the egg whites until stiff peaks form.
7. Gently fold the stiffly beaten egg whites into the batter until well combined.
8. Stir in the toasted pecans and shredded coconut.
9. Pour the batter into the prepared cake pans and bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
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