For best results in this recipe, look for whipping-quality egg whites in the refrigerator section of grocery stores; see the package for substitution equivalencies.
Yield Makes one 9-by-13-inch cake
1 1/4 cups (2 1/2 sticks) unsalted butter, room temperature, plus more for pan
4 1/2 cups sifted cake flour (not self-rising), plus more for pan
2 tablespoons baking powder
3/4 teaspoon salt
1 1/2 cups milk
1 1/2 tablespoons pure vanilla extract
2 1/4 cups sugar
7 large egg whites
Preheat oven to 350 degrees. Butter a 9-by-13-by-2-inch baking pan. Line bottom with parchment or waxed paper. Butter paper; dust with flour. Tap out excess; set aside.
Sift together flour, baking powder, and salt into a medium bowl, and set aside. Combine milk and vanilla in another bowl; set aside. Place butter in a mixing bowl; using an electric mixer, beat until pale and creamy. Add sugar in a steady stream; continue beating until mixture is light and fluffy, about 3 minutes.
Reduce speed to low. Add flour mixture in three batches, alternating with milk mixture and starting and ending with flour; beat just until combined. Do not overbeat.
In another mixing bowl, beat egg whites until stiff peaks form. Fold one-third of the whites into the batter just until combined. Fold in remaining whites in two batches.
Pour batter into prepared pan; smooth top with a spatula. Bake until a cake tester inserted near the center comes out clean and the cake springs back when pressed lightly in the center, 35 to 45 minutes.
Transfer to a wire rack; let cool in pan at least 15 minutes. Run a paring knife around sides to loosen; invert cake onto rack. Remove paper; reinvert cake to prevent splitting. Let cool completely.
This cake can be made ahead and stored, wrapped well in plastic, up to one day in the refrigerator or up to one week in the freezer. Let come to room temperature before decorating or serving.