Heat the oven: Preheat to 375°F (190°C). Lightly butter a 9-inch square baking dish or similar 2-quart dish.

Prep the berries: In a large bowl, combine blackberries, 1/2 cup granulated sugar, brown sugar (if using), lemon juice, lemon zest, and cornstarch. Gently toss to coat. Let it sit while you make the topping.

Make the batter: In another bowl, whisk flour, baking powder, salt, remaining 1/4 cup granulated sugar, and cinnamon or nutmeg (if using). Add milk, melted butter, and vanilla. Stir just until combined; it should be thick but pourable. Don’t overmix.

Layer it up: Spread the berry mixture evenly in the baking dish. Dollop the batter over the berries in large spoonfuls, leaving some gaps for juices to bubble through. Sprinkle the top with turbinado sugar if you like a crunchy finish.

Bake: Place the dish on a rimmed baking sheet to catch any drips. Bake for 38–45 minutes, until the topping is golden and the filling is bubbling around the edges.

Check doneness: Insert a toothpick into the thickest part of the topping; it should come out clean or with a few moist crumbs. The berry juices should look thick and glossy.

Rest and serve: Let the cobbler rest for 15–20 minutes to set. Serve warm with ice cream or whipped cream.