Preheat oven to 375°F. Lightly grease an 8x8-inch baking dish or a 9-inch deep dish pie plate.
In a large bowl, gently toss blackberries, granulated sugar, cornstarch, lemon juice, (lemon zest if using), vanilla, cinnamon, and salt until the berries are evenly coated. If using frozen blackberries, do not thaw them first.
Pour the blackberry mixture into the prepared baking dish. Bake uncovered for 10 minutes, just until the berries begin to release their juices.
While the filling pre-bakes, make the crispy topping. In a medium bowl, whisk together flour, granulated sugar, brown sugar, baking powder, and salt.
Stir in melted butter and vanilla until the mixture forms moist, crumbly clumps. It should look like chunky cookie crumble, not wet batter.
Carefully remove the hot blackberry filling from the oven. Sprinkle the topping evenly over the berries, leaving a few small spaces for the fruit to bubble through.
Sprinkle coarse sugar over the top.
Return to the oven and bake for 28–32 minutes, or until the topping is deeply golden and the blackberry filling is bubbling around the edges. If using frozen blackberries, bake for 32–35 minutes.
Let the cobbler cool for at least 15 minutes before serving. Serve warm with vanilla ice cream or whipped cream.