Sifted together, sugar, cornstarch, and cinnamon into a medium bowl. Whisk the mixture making sure the mixture is fully combined. Add blueberries, with your fingers toss to coat and set aside.
Add flour, baking powder, sugar, salt in a food processor bowl and pulse until combined. Add butter and pulse until mixture resembles coarse oatmeal. Transfer mixture to a large bowl, and add heavy cream and vanilla in a steady stream, mixing with a spatula until the dough comes together. Using your fingers, gather the dough and divide into 9 equal pieces, and loosely form each piece into a ball and flatten to about ½-inch thickness. Set aside.
Transfer blueberry mixture to a greased 8-inch square-baking dish. Top blueberry mixture with cobbler dough balls, spacing evenly. Brush dough with heavy cream, and sprinkle with coarse sugar or granulated sugar. Bake until berries are bubbling in center and dough toppings are golden brown, about 50-55 minutes. Transfer dish to a wire rack, and let cool slightly, about 30-40 minutes.