Preheat oven to 350 degrees. Prepare three 8" cake pans (or four 6") with pam and parchment.
In a medium bowl combine and stir the eggs, egg white, 1/4 cup of milk, and the vanilla. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, combine the dry ingredients together on low speed for 30 seconds.
Add the butter and remaining milk, and mix on a low speed until just combined. Increase to medium speed and mix for 1-2 minutes.
Scrape the sides of the bowl and begin to add the egg mixture in 2 separate batches, beat on medium speed until it is just combined.
Divide the batter between the cake pans.
Bake for 25-30 minutes (20-24 min. for 6" pans) or until a toothpick comes out clean.
Let cool on racks until cooled completely.