Preheat oven to 350°. Stir together cornstarch and 1/2 cup sugar. Toss berries with cornstarch mixture, and spoon into a lightly greased 11- x 7-inch baking dish.
Beat butter at medium speed with an electric mixer until fluffy; gradually add remaining 1 cup sugar, beating well. Add eggs, 1 at a time, beating just until blended after each addition.
Combine flour and baking powder. Stir together sour cream and baking soda. Add flour mixture to butter mixture alternately with sour cream mixture, beginning and ending with flour mixture. Beat at low speed just until blended after each addition. Spoon batter over berry mixture.
Bake at 350° for 45 minutes; shield loosely with aluminum foil to prevent excessive browning, and bake 20 to 25 minutes or until a wooden pick inserted in center of cake topping comes out clean.
Switch It Up Summer Fruit Cobbler: Substitute 3 cups coarsely chopped, peeled fresh nectarines; 2 cups fresh blueberries; and 1 cup fresh raspberries for blackberries.