Grilled Peach and Berry Pie

Name: Grilled Peach and Berry Pie
Ingredients: All-purpose flour for dusting; 3 batches basic pie dough, each flattened into a disk; 1 lb. (500 g) peaches, peeled, pitted and sliced 1/2 inch (12 mm) thick; 1 lb. (500 g) mixed whole berries, such as blackberries, blueberries and raspberries; 1 Tbs. fresh lemon juice; 1/3 cup (3 oz./90 g) granulated sugar; 2 Tbs. arrowroot starch or cornstarch; 1/4 tsp. kosher salt; Pinch of ground Ceylon cinnamon; Pinch of cayenne pepper (optional); 1 egg beaten with 1 tsp. water; Turbinado sugar for sprinkling