Blackberry Buttermilk Cake

Position a rack in middle of oven and preheat to 350 °. Butter pan; line bottom with a round of parchment paper. Butter parchment. Dust with flour; tap out excess. Arrange berries in a single layer in bottom of pan; sprinkle evenly with 1/4 cup sugar. Sift 2 1/3 cups flour, baking powder, salt, and baking soda into a medium bowl; set aside. Using an electric mixer, beat 3/4 cup butter and remaining 1 1/3 cups sugar in a large bowl at medium-high speed, occasionally scraping down sides of bowl, until pale and fluffy, about 2 minutes. Add eggs, one at a time, beating well after each addition. Beat in vanilla and zest. Reduce speed to low; beat in flour mixture in 3 additions, alternating with buttermilk in 2 additions, beginning and ending with flour mixture and beating just until incorporated. Pour batter over berries in pan; smooth top. Bake until cake is golden brown and a tester inserted into the center comes out clean, about 1 hour 25 minutes. Let cool in pan set on a wire rack for 15 minutes, then run a thin, sharp knife around edge of pan to loosen. Remove pan sides. Invert cake onto rack and remove pan bottom; peel off parchment. Dust top generously with powdered sugar and let cool completely.