Heat the oven to 400°F. Line a standard 12-muffin pan.
Cream the butter, sugar, and vanilla in a stand mixer, fitted with a paddle attachment, on medium-high speed until lightened and ultra-fluffy, about 7 minutes. Stop and scrape down the bowl as necessary—there should be no visible crystals of sugar left in the butter. Meanwhile, combine the flour, baking powder, and salt in a bowl, and stir with a fork.
Reduce the speed to low, and add in the eggs one at a time, again scraping down the sides of the bowl. (If the mixture looks curdled, it means the butter and eggs have separated—bring them back together by heating the stand mixer bowl with a torch, or with a warm, damp towel.) Increase the speed to medium, and whip until batter is webby and thickened, another 2 to 3 minutes. Reduce speed to low, and alternate adding the milk and dry ingredients until there are no traces left of either.
Fill each lined muffin cup 3/4 of the way full, using a size 16 disher or 1/4 measuring cup. Bake for 5 minutes, then drop the heat to 350°F, and bake another 22 to 25 minutes, or until the cupcakes bounce back when pressed lightly. Transfer to a wire rack to cool completely before frosting.