Preheat the oven to 350°F. Butter a 9x13-inch baking dish; set aside. In a large bowl, toss together peaches, 3/4 cup of the granulated sugar, cornstarch, vanilla, 1/2 teaspoon of the salt and cinnamon (if using); set aside.
In a food processor, pulse flour, remaining 1/4 cup granulated sugar, baking powder and remaining 1/2 teaspoon salt until combined. Add 8 tablespoons butter and shortening and pulse until pea-sized lumps remain. Add buttermilk and pulse again, just until mixture forms a rough dough.
Stir peach mixture well, then transfer to prepared dish. Drop dough onto peaches in large dollops. Melt remaining 2 tablespoons butter and brush onto dough, then sprinkle all over with turbinado sugar. Bake until peaches are tender and bubbly and biscuits are puffed and golden brown, about 1 hour. Serve warm or at room temperature.