Heat the oven to 375°F and butter a 3-quart baking dish.
Fold the blackberries with 3/4 cup sugar, cornstarch, lemon juice and 1/4 teaspoon salt, then spread them in the dish.
Whisk the flour, 1/3 cup sugar, baking powder and 1/2 teaspoon salt; rub in the butter until coarse crumbs form.
Stir the vanilla into the cream, pour it over the flour mixture and fold only until no dry pockets remain.
Drop the dough in eight loose mounds over the berries without covering the entire surface.
Bake for 40 to 42 minutes until the topping is deeply golden and the filling bubbles in the center; cool for 25 minutes.