Preheat your oven to 350°F (175°C) and lightly grease a 9×13-inch baking dish.
In a small bowl, whisk together sugar and cornstarch.
Place the blackberries in a mixing bowl, drizzle with melted butter, sprinkle the cornstarch mixture over the top, and toss until the berries are evenly coated.
Spread the blackberry mixture into the prepared baking dish, then whisk together the flour, sugar, baking powder, and salt in a separate mixing bowl.
Stir in milk, melted butter, and vanilla extract until the batter is combined but still a little lumpy and pour the batter evenly over the blackberries in the dish.
Bake in the preheated oven for 55 to 60 minutes, or until the berries are tender and the crust is golden brown.
Serve warm and enjoy.