Preheat the oven to 350 degrees F and position a rack in the middle of the oven. Line one 12-cup standard muffin tin with cupcake liners.
Sift the flour, baking powder and salt into a medium bowl. Stir the milk and vanilla together in a small bowl. Set aside.
Add the butter to the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if using a handheld electric mixer).
Mix on low speed until the butter is smooth, about 1 minute. Gradually beat in 1/2 cup of the sugar. Increase the speed to high and beat until light and fluffy, about 5 minutes. Scrape down the sides of the bowl as needed.
Reduce the mixer speed to low. Add about one-third of the flour mixture and beat until just combined. Add half the milk mixture and beat until smooth. Repeat, adding flour, then milk, and then the rest of the flour, stopping and scraping down the sides of the bowl as needed. Increase the mixer speed to medium and beat briefly to make a smooth batter.
Put the egg whites in a clean bowl. Whip on high speed until foamy. Gradually add the remaining 1/4 cup sugar and continue to beat until the egg whites are glossy and hold stiff peaks, about 10 minutes. Fold the whites into the batter in three batches. Divide the cake batter evenly between the liners.
Bake until a tester inserted in the center of the cakes comes out clean, rotating the tin about halfway through, about 20 minutes.
Cool the cupcakes on a rack in the tin for 10 minutes, and then remove from the tin. Cool on the rack completely.