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 the butter, half the brown sugar and half the cinnamon, and toss. Add the remaining butter, sugar and cinnamon to the granola in a small bowl 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 1 large scoop of ice cream into 4 bowls and top with the peache mixture. Drizzle with some of the caramel sauce.