Preheat oven to 375°F (190°C). In a 9x13 inch baking dish, gently toss together blackberries, granulated sugar, brown sugar, lemon juice, lemon zest, cornstarch, cinnamon, and a pinch of salt. Let sit for 15-20 minutes to macerate.

In a medium bowl, whisk together the flour, 1/2 cup sugar, baking powder, baking soda, and salt for the topping.

Cut the cold, cubed butter into the flour mixture using a pastry cutter or forks until it resembles coarse crumbs with some pea-sized pieces.

In a separate small bowl, combine the cold buttermilk and vanilla extract. Pour into the flour mixture and stir with a fork until just combined into a shaggy dough. Do not overmix.

Drop large spoonfuls of the dough unevenly over the top of the blackberry filling. Sprinkle the top with the remaining 1 tablespoon of granulated sugar and the coarse sugar.

Place the baking dish on a rimmed baking sheet to catch any drips. Bake for 40-50 minutes, or until the filling is bubbly and the topping is deep golden brown.

Remove from the oven and let the cobbler rest on a wire rack for at least 30-45 minutes before serving to allow the filling to thicken. Serve warm with vanilla ice cream.