Preheat oven to 350°F Butter two 9-inch round cake pans and line with circles of parchment paper, then butter parchment. (Alternately, you can use a cooking spray, either with just butter or butter and flour to speed this process up.).
Sift together flour, baking powder, baking soda, and salt in a medium bowl. In a large mixing bowl, beat butter and sugar in a large bowl with an electric mixer at medium speed until pale and fluffy, then beat in vanilla. Add eggs 1 at a time, beating well and scraping down the bowl after each addition. At low speed, beat in buttermilk until just combined (mixture will look curdled). Add flour mixture in three batches, mixing until each addition is just Incorporated.
Spread batter evenly in cake pan, then rap pan on counter several times to eliminate air bubbles. (I like to drop mine a few times from two inches up, making a great big noisy fuss.) Bake until golden and a wooden pick inserted in center of cake comes out clean, 35 to 40 minutes. Cool in pan on a rack 10 minutes, then run a knife around edge of pan. Invert onto rack and discard parchment, then cool completely, about 1 hour.