Heat oven to 375°F.
Combine the peaches, sugar, and butter in a 12-inch cast-iron skillet over medium-high heat — the skillet will be very full. Cook, stirring regularly, until the peaches have reduced by half, are very tender, and the liquid they've given up has thickened, about 45 minutes. Cool slightly while preparing the dough.
Whisk together the flour, sugar, baking powder, and salt in a large bowl. Add the buttermilk to the dry ingredients. Sir to combine. Add the 1 cup of heavy cream and stir to create a moist, but not sticky dough.Yup...you're making biscuits.
Dump the dough onto a lightly floured work surface. Gently press the disk out to a 3/4-inch thickness. Fold the dough over onto itself 3 to 4 times and then gently pat back out to a 3/4-inch thickness. Use a pizza cutter to slice the dough into 1-inch squares.
Arrange the dough pieces on top of the peaches so that they resemble cobblestones. Press the dough down into the peaches slightly. Brush the tops with the remaining cream and sprinkle generously with Demerara sugar.
Bake until the peaches are bubbling and the biscuit topping is brown, 20 to 25 minutes. Cool for 15 minutes before devouring. Serve with ice cream or whipped cream, or just use your hands.