Preheat oven to 375 degrees. In a large bowl, whisk together flour, cornmeal, baking powder, salt, and 1 cup plus 2 tablespoons sugar. In another bowl, whisk together buttermilk, eggs, and melted butter; pour over flour mixture, whisking to combine.
In a 10-inch skillet (preferably cast-iron), heat remaining tablespoon butter in the oven until melted and skillet is hot, about 5 minutes. Remove from oven; swirl to coat bottom of pan. Pour batter into skillet; scatter blackberries on top, and sprinkle with remaining 1/4 cup sugar.
Bake, with a baking sheet on rack below (to catch any drips), until top is evenly browned, 45 to 50 minutes. Let cool slightly, about 30 minutes. Run a knife around the edge to loosen; cut into 8 wedges. Serve warm or at room temperature.