Summer Berry Cobbler

Name: Summer Berry Cobbler
Ingredients: 1 pint blueberries; 1 pint raspberries; 1 pint blackberries; 1 pint strawberries, hulled and sliced in half; 1/2 cup granulated sugar, plus more, for dusting; Pinch cinnamon; 2 tablespoons cornstarch; 1/2 lemon, juiced; 1 recipe Blueberry Scone Dough, recipe follows; Melted butter; 2 cups unbleached flour, plus more for rolling berries; 1 tablespoon baking powder; 1 teaspoon salt; 1/3 cup sugar; 1/4 cup unsalted butter, chilled and cut in chunks; 3/4 cup buttermilk or cream; 1 egg; 1 pint fresh blueberries