Preheat your oven to 375°F (190°C). Lightly butter a 9x13-inch baking dish or a 10-inch cast iron skillet.
In a large bowl, gently toss the blackberries with sugar, cornstarch, lemon juice, vanilla extract, and salt.
Allow this mixture to sit for about 10 minutes, giving the berries time to release some of their juices and the flavors to meld.
Whisk together flour, sugar, baking powder, and salt in a medium bowl.
Add the cold butter and use a pastry cutter or your fingertips to blend until it resembles coarse crumbs with pea-sized bits of butter still visible.
Stir in the milk and vanilla extract just until combined – avoid overmixing. The batter should be thick but pourable.
Transfer the blackberry mixture to your prepared baking dish, spreading it evenly.
Dollop the batter over the blackberries in an even layer, leaving some small gaps for the berries to bubble through. Sprinkle with coarse sugar if desired.
Bake for 45-50 minutes until the topping is golden brown and the filling is bubbling around the edges. If the top browns too quickly, loosely cover with aluminum foil after about 30 minutes.
Allow to cool for at least 20 minutes before serving to let the filling properly set.