Cut the peaches in half and pit them. If you want to add cinnamon and/or sugar, grill entire peach halves; otherwise, you can cut them into wedges, if you like. Peeling the peaches isn't necessary for the grill, but you certainly can peel them, if you like. See How to Peel Peaches here for tips to make it easy on yourself. Lightly brush the cut side(s) of the peaches with the oil. Set the oiled peaches on the medium hot grill.