Gourmet Live's First-Birthday Cake

Heat oven to 350 °F with racks in upper and lower third. Butter cake pans, then line bottoms with rounds of wax paper or parchment and butter the paper. Dust pans with additional flour and knock out excess. Sift together flour, baking powder, baking soda, and salt into a bowl. Beat butter with sugar in a large bowl at medium-high speed (preferably using a stand mixer) until pale and fluffy, 3 to 5 minutes. Add eggs, 1 at a time, beating well after each addition. Add vanilla and beat mixture 5 minutes more. Reduce speed to low, then add flour mixture alternately with yogurt in 3 batches, beginning and ending with flour mixture and mixing just until smooth. Divide batter between pans (about 2 3/4 cups per pan), spreading evenly, then rap each pan on counter once or twice to eliminate air bubbles. Bake layers, switching position of pans and rearranging them in oven halfway through baking time, until cake begins to pull away from side of pan and a wooden pick inserted in center of each comes out clean, 15 to 20 minutes total for 9-inch pans and 20 to 25 minutes total for 8-inch pans. Cool 10 minutes in pans on racks, then run a thin knife around edge of pans and invert layers onto racks to cool completely.