Preheat oven to 350 F. Grease a 9-inch springform pan.
Whisk the flour, baking powder, baking soda, and salt together in a medium bowl. Set aside. Using a handheld mixer, beat the butter and sugar together in a large bowl until creamed, about 2 minutes. Add the egg and vanilla and beat on high speed until combined. Scrape down the bottom and sides of the bowl as needed.
With the mixer running on low speed, add the dry ingredients and milk to the wet ingredients until combined. (Make sure there are no large lumps on the bottom of the bowl.) Batter will be slightly thick. Pour the batter evenly into the prepared pan. Bake for 30-36 minutes or until a toothpick inserted in the center comes out clean. If the top begins browning too quickly in the oven, loosely place a piece of aluminum foil on top.
Allow the cake to cool completely in the pan set on a wire rack.