Preheat your oven to 350°F and line a 6-inch round cake pan with parchment paper.
Whisk together the flour, sugar, and baking powder in a medium mixing bowl.
Gently stir in the milk, applesauce, and vanilla until the batter is just smooth.
Fold in the beaten egg whites carefully using a spatula to keep the mixture airy.
Pour into the pan and bake for 22-28 minutes (until a toothpick comes out clean).
Allow the cake to cool completely before applying the frosting.