Preheat oven to 350°F. Butter and lightly flour a 5-inch cake pan (at least 3 inches tall). Line bottom with parchment paper. Set aside.
Sift together cake flour, baking powder, and salt. Set aside. In another bowl, whisk together milk, egg whites, and vanilla. Set aside.
In the bowl of a stand mixer, beat butter until smooth. Add sugar and mix until combined. Scrape down bowl as needed to ensure even mixing.
Add ⅓ of the dry ingredients. Mix on low speed while adding half of the liquid ingredients. Add another ⅓ of dry, follow with remaining liquid ingredients and end with dry ingredients. Mix until batter is evenly combined.
Spoon batter into prepared cake pan. Level off the top. Bake for 60 minutes, rotating pan midway through baking. If top of cake is browning too much, cover with foil tent. Bake until toothpick inserted in center of cake comes out clean. Cake batter will rise slightly over the 3-inch cake pan. Let cool in pan for 5 minutes before unmolding. Allow to cool to room temperature on wire rack.
Once cake is cool, use a serrated knife to slice off excess muffin top. Divide cake into three even layers.