Make the filling
In a large bowl, toss together the blueberries, blackberries, raspberries, granulated sugar, salt, lemon juice, and cornstarch. Transfer to a 10 by 14-inch rectangular, ceramic baking dish.
Make the dough and bake the cobbler
Set the oven rack in the lower third of the oven. Preheat the oven to 375°F. Line a baking sheet with parchment paper or a nonstick silicone baking mat.
In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, salt, and crystallized ginger.
Working quickly so as not to warm the butter, work the butter into the flour mixture with your fingers until it resembles coarse crumbs. Add 6 Tbs. of the buttermilk and fold with a rubber scraper or your hands until the buttermilk has been absorbed and there are no dry patches. Add the remaining 2 Tbs. of buttermilk as necessary (you won’t use all of it; reserve what’s left for brushing the dough). The dough should be dry enough to hold a shape when you cut it out.
Turn the dough out onto a lightly floured work surface. With lightly floured hands, pat the dough to about 3/4 inch thick. Cut out twelve stars with a 3-3/8-inch (measuring point to point) star cookie cutter and place them in a single layer on top of the fruit. Brush the stars with the reserved buttermilk, and sprinkle each with 1/4 tsp. of sanding sugar. Bake, rotating the baking sheet two-thirds of the way through the baking time, until the biscuit topping is lightly browned and cooked through, 60 to 65 minutes. Serve warm or at room temperature.