Preheat oven to 350° and set oven rack to the middle position. Grease and flour two 8- or 9-inch cake pans.
Using a stand or hand mixer, cream the butter and sugar until pale and very fluffy, about 7 minutes. Add eggs one at a time, beating well after each addition. Add the vanilla and beat well.
In a bowl, whisk together the flour, baking powder, and salt. Add 1/3 of the flour mixture to the butter-sugar mixture and mix on low until combined. Add half the milk and stir. Repeat. Add the remaining third of the flour mixture and stir just until smooth.
Divide the batter equally among the prepared pans, then bang the pans on your counter to remove any air bubbles. Bake for 30 to 35 minutes, or until the cakes are golden brown and just beginning to pull away from the sides. Cool for 5 minutes, then remove and cool completely on wire racks, covering the cakes with plastic wrap or a kitchen towel.
Once cool, you are ready to assemble the cake and frost with icing of your choice.