Preheat your oven to 350°F (175°C). Grease and flour two 8-inch round cake pans.
In a bowl, whisk together the flour, baking powder, and salt.
In a large mixing bowl, beat the butter and sugar until light and fluffy.
Add the eggs and egg whites one at a time, mixing well after each.
Stir in the vanilla extract.
Add the dry ingredients in three parts, alternating with milk, beginning and ending with the flour mixture.
Divide the batter evenly between the prepared pans.
Bake for 25–28 minutes, or until a toothpick inserted in the center comes out clean.
Let the cakes cool in the pans for 10 minutes, then turn out onto a wire rack to cool completely before frosting.