Preheat oven to 350 degrees Fahrenheit. Spray 2 9-inch round cake pans with non-stick cooking spray, line each pan with parchment circles, grease again, and flour. Set aside.
In a large liquid measuring cup, whisk together egg whites, milk, and vanilla.
In the bowl of an electric mixer, using the paddle attachment, combine flour, sugar, baking powder, and salt, until well blended. You can also use a whisk to combine the mixture.
On low speed, add the softened butter, and blend until incorporated. Lumps will form.
Add liquid ingredients in two stages, stopping the mixer and scraping down the sides of the bowl with a rubber spatula after each addition. Batter should be thick and smooth. Put mixer on medium-high speed for about 5-10 seconds to thoroughly blend all ingredients.
Divide batter between the 2 prepared cake pans.
Bake for approximately 25-30 minutes, or until a small, sharp knife inserted in the center of each cake comes out clean.
Remove cakes from pans when barely warm and place on cooling racks or cardboard cake circles. Frost as desired.