Preheat the oven to 350 degrees . Grease and flour two 9-inch round cake pans. Line the pans with parchment and grease the parchment. In a medium bowl, combine the flour, baking powder and 1/2 teaspoon salt.
Using an electric mixer, beat 2 sticks butter and the granulated sugar at medium speed until fluffy, about 5 minutes. Stir in 1 tablespoon plus 1 teaspoon vanilla and a pinch salt. Gradually add the egg whites, beating on low speed and scraping the side of the bowl. Beat at high speed for 1 minute until smooth. Mixing at low speed, add the flour mixture in 3 parts, alternating with 1 cup milk. Beat at medium speed until smooth, about 30 seconds.
Transfer the batter into the prepared pans. Bake until a toothpick inserted into the center of the cake comes out clean, about 40 minutes. Let cool for 10 minutes, then invert the layers onto a rack, discard the parchment and let cool completely.
Meanwhile, using an electric mixer, combine the remaining 2 sticks butter and the confectioners sugar at low speed. Gradually add the remaining 2 tablespoons milk and 2 teaspoons vanilla and beat at high speed until fluffy, about 5 minutes.
Transfer 1/4 cup of the frosting to a small bowl. Add enough food coloring to make a vivid red. Place 1 cake layer on a platter. Spoon a large dollop of plain frosting in the center of the layer and spread to within 1/4 inch of the edge. Place the second layer on top of the first and frost the top and side with the remaining plain frosting. Using a resealable plastic bag with one corner snipped off, pipe the red frosting onto the cake to look like baseball stitching.