Preheat oven to 400°.
Combine first 3 ingredients in a large bowl. Combine 1/2 cup granulated sugar, cornstarch, cinnamon, and nutmeg (if desired) in a small bowl. Add sugar mixture to fruit, tossing to coat. Spoon fruit mixture into an 11 x 7-inch baking dish.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, 1/4 cup granulated sugar, baking powder, and baking soda in a large bowl. Cut in butter with a pastry blender or 2 knives until the mixture resembles coarse meal. Combine buttermilk and egg in a small bowl; stir with a whisk. Add buttermilk mixture to flour mixture; stir until moist.
Drop dough by spoonfuls onto fruit mixture to form 8 dumplings. Sprinkle with turbinado sugar, if desired. Cover and bake at 400° for 35 minutes; uncover and bake an additional 15 minutes or until browned.