Preheat the oven to 350°F. Line the bottoms of two 9-inch cake pans with parchment paper and spray only the parchment with nonstick cooking spray. Do not spray the sides of the pans.
In a stand mixer fitted with a paddle attachment, combine the flour, sugar, baking powder, and salt. Stir to mix.
Add the butter and beat on medium speed for 1 minute until the mixture becomes coarse.
Reduce the mixer speed to low and add the buttermilk and vanilla. Mix for 1 minute until combined, then increase to medium speed and beat for 30 seconds. Scrape down the sides of the bowl.
With the mixer on low speed, add the eggs one at a time, mixing each until incorporated. Add the egg whites and beat on medium-high speed for 30 seconds until the batter is smooth.
Divide the batter evenly between the prepared pans and smooth the tops.
Bake for 25 to 30 minutes, or until the edges are golden brown and a toothpick inserted into the center comes out clean.
Remove from the oven and let the cakes cool in the pans for 5 minutes before transferring them to a wire rack to cool completely.