Heat the Oven – Set the oven rack to the middle position. Preheat to 400ºF (204ºC).
Grease Baking Dish – Grease a 9" square baking dish with softened butter or cooking spray. Set on top of a parchment paper or foil-lined sheet pan. Set aside.
Prepare the Filling – In a large bowl, whisk together sugar, cornstarch, lemon zest, cinnamon, and salt. Add the blackberries, lemon juice, and vanilla. Stir until evenly coated. Spread the filling into the baking dish.
Prepare the Topping – In a medium bowl, whisk together flour, sugar, baking powder, salt, and baking soda. Toss the cold cubed butter into the flour mixture. Use your fingers to break into small pea-sized pieces until the mixture resembles crumbly cornmeal. Stir in the buttermilk. The topping will be wet and look like a very thick cake batter.
Assemble the Cobbler – Drop about 2 tablespoon-sized mounds evenly on top of the blackberry filling, about 16 mounds. In a small bowl, combine 1 tablespoon sugar, ¼ teaspoon cinnamon, and ⅛ teaspoon ginger. Evenly sprinkle over the topping and filling.
Bake the Cobbler – Bake until the topping is golden brown and the filling is bubbly on the sides of the baking dish, about 30 to 35 minutes. The filling should reach between 200 to 203ºF (93 to 96ºC) to fully thicken.
To Serve – Cool the cobbler for 20 to 30 minutes before serving to allow the filling to thicken. Serve with a scoop of ice cream or whipped cream if desired.
Notes
Using Flour to Thicken the Filling: Add 1/4 cup of flour instead of 2 tablespoons of cornstarch.
Using Frozen Blackberries: Do not defrost. Follow all directions, except extend cook time by about 5 minutes. Loosely tent with foil if the topping is browning too quickly.
Storing: Cool, cover, and refrigerate the cobbler for up to 2 days.
Reheating: Bake in a 375ºF (191ºC) oven until the filling and biscuit topping is warm, about 15 to 25 minutes. This varies depending on whether you are reheating the entire baking dish or just a portion of it. Reheat individual portions in the microwave in 30-second intervals on high power, 60 to 90 seconds.