Preheat oven to 325 and grease extra well (or line with parchment and grease parchment) 2 9 inch round cake pans, 3 8 inch round cake pans, or one 8 x 12 oblong pan or one standard bundt pan*.
In a stand mixer, cream butter and add in sugar gradually. Cream until sugar is smooth. Add in one egg at a time and mix until fluffy.
Mix the flour with the baking powder and salt.
Alternate adding in the flour mixture and milk.
Stir in vanilla.
Spread batter evenly in cake pan, then tap pan on counter several times to eliminate air bubbles. (I like to drop mine a few times from two inches up, making a great big noisy fuss.) Bake until golden and a wooden pick inserted in center of cake comes out clean, 35 to 40 minutes. Cool in pan on a rack 10 minutes, then run a knife around edge of pan. Invert onto rack and discard parchment, then cool completely, about 1 hour.
Notes
This cake can be made in a variety of pans. You can use 3 8 inch round cake pans, 2 9 inch round cake pans, one 8 x 12 oblong pan, or one standard bundt pan. Make sure to grease the pans well especially if you're using a bundt pan!!