Preheat oven to 350 degrees F (175 degrees C). Lightly grease an 8-inch square baking pan. Line bottom with parchment or wax paper, or dust lightly with flour.
Sift together the flour, salt, and baking powder.
Beat butter and white sugar until fluffy and light in color. Gradually add eggs, beating well after each addition; stir in vanilla. Add the sifted dry ingredients to the creamed mixture alternately with the milk. Stir until just blended (see Cook's Note for Blueberry Cake variation). Pour batter into prepared pan.
Bake at 350 degrees F (175 degrees C) for until cake springs back when lightly touched, about 30 minutes. Let cool in pan for 10 minutes before inverting onto wire rack to cool completely.