Preheat oven to 350°F. Grease three 9-inch cake pans, line with parchment paper rounds, then grease the parchment paper.
Whisk the cake flour, salt, baking powder, and baking soda together. Set aside.
Using a stand mixer fitted with the whisk attachment, beat the butter and sugar together on high speed until smooth and creamy, about 3 minutes. Scrape down the sides and up the bottom of the bowl with a silicone spatula as needed.
Beat in the 3 eggs, 2 egg whites, oil and vanilla extract on high speed until combined, about 2 minutes. Scrape down the sides and up the bottom of the bowl as needed.
With the mixer on low speed, add the flour, salt, baking powder and baking soda until combined.
With the mixer still running on low, pour in the buttermilk and mix just until combined. You may need to whisk it all by hand to make sure there are no lumps at the bottom of the bowl. The batter will be slightly thick.
Pour batter evenly into cake pans. Bake for around 24-26 minutes or until the cakes are baked through. To test for doneness, insert a toothpick into the center of the cake. If it comes out clean, it’s done.
Allow cakes to cool completely in the pans set on a wire cooling rack. The cakes must be completely cool before frosting and assembling.