Preheat the oven to 350° F. Line cupcake pans with 20 paper liners.
Sift the cake flour, baking powder and salt. Set aside.
In a mixer fitted with the paddle attachment, cream the butter, sugar and vanilla on medium speed until light and fluffy, about 2 minutes. Mix in the eggs one at a time, scraping well after each addition. With the mixer on low speed, add the milk and flour mixture alternately, beginning with the milk and ending with the flour.
Scoop the batter into the cupcake liners, filling them just below the rim. (I use a 2-ounce ice cream scoop.) Bake in the center of the oven for 17 to 18 minutes, until a toothpick comes out clean. Cool for 10 minutes, remove from the pans, and allow to cool completely before frosting.