Brush peach halves with oil. Arrange a charcoal or gas grill for indirect grilling. Place halves, cut sides down, on the rack over the heat. Grill directly over medium heat, covered, for 3 minutes. Remove. Cut peach halves into 1/2-inch thick slices. In a very large bowl toss peaches with granulated sugar, cornstarch, and lemon juice.
Grease a 9- or 10-inch cast iron skillet and line with one of the piecrusts. Spoon peach mixture into crust-lined skillet. Spoon dulce de leche in mounds over filling. Sprinkle with salt. Cut slits in second crust and place over filling. Tuck dough down sides of skillet. Crimp edge as desired. Brush pastry with egg and sprinkle with coarse sugar.
Place the skillet on rack over unlit side of the grill. Cover and grill for 45 to 50 minutes or until crust is golden and filling is bubbly, rotating once halfway through grilling. Remove and cool on a wire rack at least 2 hours before serving. If desired, serve with ice cream and garnish with mint leaves.