Preheat an oven to 350 degrees F (175 degrees C). Grease two 9-inch round cake pans with butter. Line the bottoms with parchment paper, then grease the parchment paper. Sift together the cake flour, baking powder, baking soda, and salt in a bowl.
Beat the butter and sugar with an electric mixer in a large bowl until light and fluffy. The mixture should be noticeably lighter in color. Add the room-temperature eggs one at a time, allowing each egg to blend into the butter mixture before adding the next. Beat in the vanilla with the last egg. Pour in the flour mixture alternately with the buttermilk, mixing until just incorporated. Pour the batter into the prepared pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 35 to 40 minutes. Cool in the pans for 10 minutes, then run a paring knife between the cake and the edge of the pan. Hold the cake pan on its side and gently tap the sides of the pan against the counter to loosen it. Cover the cake pan with a plate or cooling rack, and invert it to tip the cake out of the pan and onto the plate.