Meanwhile, rinse blackberries under cool water; drain. In 2-quart saucepan, mix 1 cup of the sugar and the cornstarch; stir in blackberries. Cook over medium-high heat until mixture comes to a boil. Cook 5 to 6 minutes, stirring frequently, until mixture is thickened and syrupy. Remove from heat; cool 15 minutes. Refrigerate until mixture is chilled, 30 minutes.