Preheat your oven to 350°F (175°C). Grease and flour your cake pans.
In a mixing bowl, combine flour, baking powder, and salt. Set aside.
In another bowl, beat the butter and sugar until light and fluffy. Add egg whites one at a time, beating well after each addition. Stir in vanilla extract.
Alternate adding the flour mixture and milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined.
Pour batter into prepared pans. Bake for 25-30 minutes or until a toothpick inserted into the center comes out clean. Cool in pans for 10 minutes, then remove to wire racks to cool completely.