1. Preheat oven to 350°.
2. Melt 1 tablespoon butter in a 10-inch cast-iron skillet over medium heat; sprinkle brown sugar evenly in pan. Remove from heat. Arrange peach slices in a circle in center of pan; scatter blueberries and raspberries evenly around peach slices. Set aside.
3. Place remaining 1/4 cup butter and granulated sugar in a large bowl; beat with a mixer at medium speed until well blended. Add rind, juice, egg whites, and egg; beat well. Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, and salt, stirring well with a whisk. Add flour mixture and buttermilk alternately to sugar mixture, beginning and ending with flour mixture.
4. Carefully spoon batter over fruit mixture. Bake at 350° for 35 minutes or until a wooden pick inserted in the center comes out clean. Run a knife around the edges of pan. Cool cake completely in pan on a wire rack. Place a plate upside down over skillet; carefully invert onto plate.