Heat the oven to 375°F and butter a 9-by-13-inch baking dish.
Toss the peaches with 3/4 cup sugar, cornstarch, lemon juice, cinnamon and 1/4 teaspoon salt in the dish; bake for 12 minutes while making the topping.
Whisk the flour, 1/4 cup sugar, baking powder and 1/2 teaspoon salt, then cut in the cold butter until pea-size pieces remain.
Stir in the buttermilk just until a shaggy dough forms.
Drop eight rough portions of dough over the hot fruit, leaving gaps for steam, and sprinkle with coarse sugar.
Bake for 30 to 35 minutes until the biscuits are browned, their centers are cooked and peach filling bubbles through the gaps; rest 25 minutes.