In a saucepan, combine blackberries, sugar, lemon juice, and cornstarch. Cook over medium heat until the mixture starts to bubble and thicken, about 5-7 minutes.

In a mixing bowl, whisk together flour, baking powder, and salt. Cut in the cold butter until the mixture resembles coarse crumbs. Stir in the milk until just combined.

Pour the blackberry filling into a baking dish. Drop spoonfuls of the dumpling dough over the filling. Cover the dish with foil.

Bake in a preheated oven at 350°F (175°C) for 25-30 minutes, until the dumplings are cooked through and golden.