Preheat the oven to 375 degrees F (190 degrees C). Grease and flour two 9 inch round cake pans. Sift the cake flour and baking powder into a bowl and set aside.
In a large bowl, beat the butter and sugar until light and fluffy, up to 10 minutes. Mix in eggs one at a time, fully blending each one in before adding the next. Stir in vanilla. Stir in the flour and baking powder, alternating with the milk until the batter is smooth. Divide the batter evenly between the prepared pans. Tap the bottoms of the pans on the counter a few times to remove air bubbles.
Bake in the preheated oven until a knife inserted into the center of the cakes comes out clean, 25 to 30 minutes. Cool cakes in the pans set over a wire rack.