Preheat oven to 375°F and butter a 9x13-inch baking dish.
In a large bowl, gently toss blackberries with 1 cup sugar, cornstarch, lemon juice, and vanilla extract. Spread evenly in the prepared baking dish.
In another bowl, whisk together flour, 1/2 cup sugar, baking powder, salt, and cinnamon.
In a separate bowl, whisk together melted butter, milk, and egg. Pour wet ingredients into dry ingredients and stir just until combined.
Drop large spoonfuls of batter over the blackberries, spreading gently to cover most of the fruit. Sprinkle coarse sugar over the top.
Bake for 35-40 minutes until topping is golden brown and blackberry juices are bubbling thickly around the edges. Cool for 20 minutes before serving.