While the grill is preheating cut the peaches in half lengthwise and remove the pits. Place the peaches on the grill, flat side down, and grill for about 5 minutes.
Flip the peaches (using tongs) and grill the other side for a few more minutes.
Place the grilled peaches on a plate or serving dish and add 1 small scoop of vanilla ice cream in the middle of each peach. Sprinkle with cinnamon and enjoy immediately!