Preheat the oven to 350 degrees. Butter a 9-by-13-inch baking dish. Make the biscuits: Whisk the flour, granulated sugar, baking powder, nutmeg and salt in a medium bowl. Add the butter and work it in with your fingers until it is in pea-size pieces. Stir in the heavy cream until the mixture just comes together into a shaggy dough. Turn out onto a floured baking sheet and pat until 1/4 inch thick; freeze until firm, about 10 minutes.
Make the filling: Toss the peaches, granulated sugar, cornstarch, orange zest and juice, and vanilla in a bowl until the peaches are coated. Gently stir in the berries. Transfer to the prepared baking dish.
Cut out circles from the cold dough using 2 1/2-inch cookie cutters. Arrange the circles on the fruit mixture; brush with heavy cream and sprinkle with coarse sugar. Bake until the biscuits are golden brown and the filling is bubbling, 50 minutes to 1 hour. Transfer to a rack and let cool.
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