Heat oven to 350 degrees. Butter three 6-by-2-inch round baking pans. Line with parchment; butter; dust with flour.
Sift flour, baking powder, and salt together in a medium bowl. With electric mixer, beat butter on medium-high speed until light and fluffy, 4 minutes. Add sugar; beat well. Reduce speed to medium; add eggs one at a time, beating well after each. Reduce speed to low; alternately add flour and buttermilk, starting and ending with flour. Stir in zest.
Pour batter into pans; bake, rotating halfway through, until tester inserted into center comes out clean, about 30 minutes. Cool in pans on rack 15 minutes. Remove; let cool completely right side up on rack.