Preheat Grill: Prepare the grill for direct or one zone cooking. Target the temperature over the heat at 400 degrees Fahrenheit.
Prepare Peaches: Cut peaches with a pairing knife along seam, cutting from the stem and vertically along the peach from one side of the stem to the other in one motion. Cut along the pit so the two hemispheres are equal in size. Using the knife, carefully cut along the pit and remove with a small spoon.
Grill Peaches: Coat the flesh side of the peaches with olive oil using a brush and place the peaches over direct heat. Grill over direct heat for 4-6 minutes or until the peaches have grill marks and have softened a bit. See note below for ripeness considerations.
Serve: Remove the peaches from the grill and serve warm with one scoop of ice cream and a drizzle of honey. Finish with some of the crushed graham cracker and a small amount of mint. Serve immediately.
Notes
Note: The riper the peaches are, the softer they will be. Ideally when buying peaches you want them slightly firm. With the slightly firm peaches you need to grill them long enough to soften them which can be up to 5 - 7 minutes and why the lower grill heat. For riper (or really soft peaches), because they are already softened, you can bring the temperature of the grill to 500 degrees Fahrenheit to get the grill marks quickly so as not to cook the peaches too much.