Heat the grill to medium.
Place apples in a medium bowl and toss with the oil. Place the apples on the grill, cut-side down and grill until nicely browned. Flip the apples over and continue to grill until nicely browned on skin side. Remove from the grill and allow to cool briefly.
Once they are cool enough to handle, core and cut the apples into wedges. Place the apple wedges into a bowl and toss with 1/2 teaspoon ground cinnamon, 4 tablespoons light brown sugar and 1/2 stick melted butter.
In another bowl, toss together the remaining melted butter, cinnamon, light brown sugar and the granola.
Place 1 large scoop of ice cream into 4 bowls and top with the apple mixture. Sprinkle the granola mixture over the top of the apple and drizzle with some of the caramel sauce, if using.