Preheat the oven to 350°F. Grease three 8-inch cake pans and line the bottoms with parchment paper.
In a medium bowl, whisk together the flour, salt, baking powder, and baking soda. Set aside.
In a large mixing bowl, beat the softened butter and granulated sugar together until very light and fluffy, about 3 to 5 minutes.
Add the eggs one at a time, mixing well after each addition.
Add the egg whites and mix until fully incorporated.
Mix in the vanilla extract.
Add half of the dry ingredients and mix on low speed until just combined.
Pour in half of the buttermilk and mix gently.
Add the remaining dry ingredients, followed by the remaining buttermilk, mixing only until incorporated.
Scrape down the sides and bottom of the bowl as needed.
Divide the batter evenly between the prepared pans.
Bake for 28 to 32 minutes, or until the tops spring back lightly when touched, the edges begin to pull slightly away from the pans, and a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for 10 to 15 minutes before turning them out onto wire racks to cool completely.