Pre-heat oven to 350 degrees. Grease and flour three 6-inch cake pans and set aside
In a small mixing bowl or liquid measuring cup, stir together the egg whites, vanilla, and ¼ cup milk and set aside.
Sift together the flour, sugar, baking powder, and salt into the bowl of an electric mixer. With the paddles attachment, mix on low until combined. Add the butter and remaining ½ cup milk and mix on low until the dry ingredients are moistened. Turn the mixer to medium-high and mix until combined. Stop the mixer and scrape down the bowl.
With the mix running on medium-low, gradually stream in the egg white mixture. Work in about 3 batches, making sure everything is incorporated before adding in more liquids, scraping the bowl in between additions.
Evenly distribute the batter between the prepared pans. Bake for 24 to 26 minutes, or until a toothpick inserted into the center of the cake comes out clean. Cool on a wire rack for 10 to 15 minutes before removing the cakes from their pans.