Adjust oven rack to middle position and preheat oven to 350 degrees. Grease an 8-inch round cake pan and line with parchment paper. Grease parchment paper and flour pan.
In a small bowl, mix milk, vanilla, and egg whites together. Set aside. In a standing mixer fitted with a paddle attachment or with an electric mixer by hand, mix together flour, sugar, baking powder, and salt on low speed until combined. Add butter, one piece at a time, and mix until only pea-sized pieces remain, about 1 minute.
To the mixing bowl, add half of the milk mixture and increase speed to medium-high. Beat until the mixture is light and fluffy, about 30 seconds. Add remaining milk mixture and beat on medium-low speed until incorporated, about 15 seconds. Do not over mix. Give the batter a final stir by hand.
Pour batter into prepared pan and smooth the top using a rubber spatula. Bake until top is light golden and a wooden toothpick inserted into the center of the cake comes out clean, about 20 to 25 minutes. Rotate pan halfway through to ensure even baking.
Cool cake in pan on a wire rack for 10 minutes. Remove cake from pan and allow to cool completely before frosting, about 2 hours.