Heat the grill to medium.
Place the peaches cut side down on the grill until browned. Remove from the grill, cut into wedges and place into a gratin dish. To the peaches add half of the butter, half the brown sugar and half the cinnamon, and toss. In a small bowl, add the remaining butter, sugar and cinnamon to the granola and toss until combined, adding more butter if needed. Top the peaches with the granola mixture and place the gratin dish onto the grill. Close and bake until the peaches and granola are golden brown, about 15 minutes.
Place one large scoop of ice cream into 4 bowls and top with the peach mixture. Drizzle with some of the caramel sauce.