In a mixer at medium speed, cream butter, sugar, and salt together until light and fluffy.
Add eggs one at a time while the mixer is running, making sure each egg is totally mixed in before adding another.
Beat mixture until light and fluffy, making sure to scrape the sides and bottom of the mixing bowl carefully.
In a separate mixing bowl, combine flour and baking powder using a wire whisk to sift and combine them. In another separate bowl, mix the milk and vanilla.
Alternate adding wet and dry ingredients to butter mixture, starting and ending with the dry ingredients. Do not overmix, as batter should be thick and fluffy. Spoon into lined cupcake pans, filling each cup about 2/3 full. Bake at 350 degrees for 12-14 minutes or until done.