Preheat oven to 375°F; butter a 9x13-inch dish.
Gently toss blackberries with 1 cup sugar, cornstarch, lemon juice, and vanilla in a large bowl; spread evenly in dish.
Whisk flour, 1/2 cup sugar, baking powder, salt, and cinnamon in another bowl.
Whisk melted butter, milk, and egg in a separate bowl; stir into dry ingredients just until combined.
Drop large batter spoonfuls over berries; gently spread to cover most fruit. Sprinkle with coarse sugar.
Bake 35-40 minutes until topping is golden brown and berry juices bubble thickly at edges. Cool 20 minutes before serving.