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1
Preheat oven to 350 degrees. Butter two 9-by-2-inch round cake pans; line bottoms with parchment paper rounds. Butter parchment, and dust with flour, tapping out excess; set aside.
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2
Into a medium bowl, sift together flour, baking powder, and salt; set aside. In the bowl of an electric mixer fitted with the paddle attachment, beat butter and 2 cups sugar until light and fluffy, 3 to 4 minutes, scraping down sides of bowl as needed. Beat in vanilla. With mixer on low speed, add flour mixture in three parts, alternating with milk and beginning and ending with flour; beat until just combined. Transfer mixture to a large bowl; set aside.
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3
In the clean bowl of an electric mixer fitted with the whisk attachment, beat egg whites on low speed until foamy. With mixer running, gradually add remaining 1/4 cup sugar; beat on high speed until stiff, glossy peaks form, about 4 minutes. Do not overbeat. Gently fold a third of the egg-white mixture into the butter-flour mixture until combined. Gently fold in remaining whites.
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4
Divide batter evenly between prepared pans, smoothing with an offset spatula. Bake, rotating pans halfway through, until cakes are golden brown and a cake tester inserted in centers comes out clean, 30 to 35 minutes. Transfer pans to a wire rack to cool 20 minutes. Invert cakes onto rack; peel off parchment. Reinvert cakes, and let them cool completely, top sides up.
