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 the vanilla extract.
Gradually add the flour mixture to the butter mixture, alternating with milk. Beat until just combined.
Pour the batter into the prepared pans and bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Let cool in pans for 10 minutes, then transfer to a wire rack to cool completely.