Whisk together flour, baking powder, and salt in a medium bowl; set aside. Put butter and sugar in the bowl of an electric mixer fitted with the paddle attachment; cream on medium-high speed until pale, 2 to 3 minutes. On medium speed, add eggs one at a time, mixing well after each addition. Add vanilla, and mix, scraping down sides of bowl. With the mixer on low speed, add the flour mixture in three batches, alternating with two batches of milk. Stir with a rubber spatula until the batter is evenly blended.