Preheat the oven to 400 degrees F (200 degrees C). Grease an 8-inch springform pan.
Sift flour and baking powder into a medium bowl and set aside.
Beat butter and sugar with an electric mixer until light and fluffy, about 3 minutes. The mixture should be noticeably lighter in color. Add eggs one at a time, allowing each egg to blend into butter mixture before adding the next. Beat in vanilla. Add flour mixture in batches, alternating with milk, mixing batter briefly after each addition just to combine.
Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 20 minutes. Cool the cake in the pan for 10 minutes, then turn the cake out onto a wire rack to cool completely.