Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9×13-inch baking dish.
Prepare the berries: Whisk sugar and cornstarch together in a small bowl. Place blackberries into a mixing bowl and drizzle with melted butter. Sprinkle cornstarch mixture over top, then toss until evenly coated. Spread into the prepared baking dish.
Make the batter: Whisk flour, sugar, baking powder, and salt together in a mixing bowl until evenly blended. Stir in milk, melted butter, and vanilla until combined but still slightly lumpy. Pour over berries in the baking dish.
Bake in the preheated oven until berries are tender and the crust is golden brown, 55 to 60 minutes.
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