Heat oven to 375°F; butter a 3-quart baking dish.
Fold blackberries with 3/4 cup sugar, cornstarch, lemon juice, and 1/4 teaspoon salt; spread in dish.
Whisk flour, 1/3 cup sugar, baking powder, and 1/2 teaspoon salt. Rub in butter until coarse crumbs form.
Stir vanilla into cream; pour over flour mixture. Fold just until no dry pockets remain.
Drop eight loose dough mounds over berries, leaving surface partly uncovered.
Bake 40 to 42 minutes until topping is deeply golden and center filling bubbles. Cool 25 minutes.