Preheat the oven to 350F and spray the bottoms of three 8-inch cake pans with non-stick spray.
In a large bowl, measure out the sugar. Scrape the seeds from the vanilla bean pod and use your fingers to rub the seeds into the sugar until very fragrant and the seeds are evenly dispersed throughout the sugar.
Set a fine mesh sifter over the bowl of sugar, and sift in the cake flour, baking powder and salt. Use a whisk to combine the dry ingredients well.
In another large bowl, whisk together the eggs, egg whites, buttermilk, melted butter, oil and vanilla extract until smooth.
Add the dry ingredients to the wet, and whisk until combined and smooth, about 10-15 seconds. Divide the batter between the cake pans. Tap a few times against the counter to pop any large air bubbles.
Bake the cakes for about 21-25 minutes, or until a cake tester or a toothpick comes out clean, and the tops spring back when lightly touched.
Set the pans on a wire rack, cover them loosely with a clean kitchen towel, and cool completely before frosting. When ready to frost and assemble the cake, remove the cakes from the pans.