Preheat oven to 325 degrees F (165 degrees C).
Mix blackberries and 1 cup sugar together in a bowl; let stand until mixture becomes juicy, 5 to 10 minutes.
Place butter in a 9x13-inch baking dish and put dish in the preheating oven until butter is melted, 2 to 5 minutes. Remove dish from oven.
Combine remaining 1 cup sugar, milk, flour, baking powder, and salt in a large bowl until batter is smooth; pour over melted butter. Do not stir. Spoon blackberry mixture over batter.
Bake in the preheated oven until bubbling and cooked through, about 1 hour.