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In a medium bowl, whisk 1 cup sugar with the flour and milk. Whisk in the melted butter.
Rinse the blackberries and pat them dry. Pour the batter into the baking dish. Sprinkle the blackberries evenly over the top of the batter. Sprinkle 1/4 cup sugar over the blackberries. Bake until golden brown and bubbly, about 1 hour. When 10 minutes of the cooking time remains, sprinkle the remaining 2 tablespoons sugar over the top. Top with whipped cream or ice cream . . . or both!