Heat grill pan on stove over medium heat.
Cut peaches in half and remove pit. Use brush to lightly coat with olive oil.
Place peach (interior side down) on the grill pan - at an angle if you want diagonal grill marks. Allow to cook for about 7 minutes. Use prongs to test if the peach flesh gives a little, without falling apart. Less ripe peaches will take longer to grill.
While still on grill pan, coat the back with a little more olive oil. Flip on back side and allow to grill for a few additional minutes.
Sprinkle with cinnamon and remove from pan. Top with ice cream scoop and a little more cinnamon. Enjoy!