Preheat the oven to 325 degrees. Line two 8 or 9-inch cake pans with parchment paper and nonstick cooking spray. Set aside.
Whisk together the dry ingredients in a large bowl. Set aside.
In a separate bowl, mix together the vanilla and buttermilk. Set aside.
In a stand mixer, combine butter, oil, and sugar. Add in the eggs and egg whites and beat until fluffy.
Starting and ending with the dry ingredients, alternate adding and mixing in the dry ingredients with the buttermilk mixture. Fold in the pecans and shredded coconut by hand.
Divide the batter between the two prepared cake pans. Bake 30-40 minutes in the lower 2/3rds of the oven. The cake is done when a toothpick can be inserted and comes out mostly clean.
Cool the cakes 15-20 minutes in cake pans before transferring to cooling racks. Cool completely before decorating.
For the Cream Cheese Frosting
Mix all ingredients together until completely combined and smooth. Be sure to scrape the sides of the bowl and stir again.
Assembly
Once cakes are cooled, slice in half lengthwise with a serrated bread knife. You should be left with four thin layers.
Place one layer onto the preferred serving platter. Top with about 3/4 cup of cream cheese frosting. Spread to the edges of the cake.
Top with another cake layer and continue frosting until all four sliced are stacked with frosting in between.
With the remaining frosting, frost the exterior of the cake.