Prepare your campfire or camp stove for cooking. You need a bed of hot coals if using a fire, or a steady medium heat on a stove.
In a large bowl, gently mix the blackberries, 1/2 cup sugar, cornstarch, and lemon juice. Set aside.
In another bowl, whisk together the flour, 1/2 cup sugar, baking powder, and salt. Cut in the cold butter with a fork or your fingers until the mixture looks like coarse crumbs. Stir in the milk just until a soft dough forms.
Line a 10-inch Dutch oven with foil or lightly grease it. Pour the berry mixture into the bottom. Drop spoonfuls of the biscuit dough over the top, spacing them evenly.
Cover the Dutch oven with its lid. Using a lid lifter, place the Dutch oven on a bed of about 8-10 hot coals. Arrange another 12-15 coals on the lid. If using a stove, set the heat to medium and cover with a lid.
Cook for 25-30 minutes, rotating the Dutch oven a quarter turn every 10 minutes to prevent hot spots. The cobbler is done when the berries are bubbly and the topping is golden brown and cooked through.
Carefully remove the Dutch oven from the heat using heavy gloves and a lid lifter. Let it cool for 5 minutes before serving. Spoon into bowls and enjoy warm.