Set a rack in the middle of the oven and heat to 400°F (205°C). Place a foil-lined baking sheet on the rack below. Lightly butter a 9x13 inch baking dish.

In a large bowl, whisk together the sugar, cornstarch, flour, lemon zest, and salt. Add the blackberries, lemon juice, and vanilla and fold gently until the berries are coated.

Spread the filling in the prepared dish, dot with the butter, and bake uncovered for 10 minutes until the juices begin to release.

While the fruit bakes, whisk the flour, sugar, baking powder, baking soda, and salt in a medium bowl. Grate the cold butter into the flour and toss until it looks like coarse crumbs with some pea-sized pieces.

Pour in the buttermilk and stir with a fork just until no dry flour remains. The dough will be sticky and shaggy. Do not overmix.

Remove the dish from the oven. Drop the dough in 8 to 10 rough mounds over the hot fruit, leaving gaps between them. Brush with cream and sprinkle with turbinado sugar.

Bake for 30 to 35 minutes until the biscuits are deep golden and the filling bubbles thickly in the center. A thermometer in the thickest biscuit should read 200°F (93°C). Tent with foil if the tops brown too fast.

Cool on a wire rack for 20 minutes before serving. Serve warm with ice cream or whipped cream.