In a food processor, combine basil, oil, orange juice and honey. Mix until the basil is very finely chopped.
Pour marinade over peaches and, if you have time, allow to sit at room temp for 30 minutes or so. If you don’t have the time, skip to the next step.
Liberally grease your grill. Place peaches on the grill cut side down. Cook for 7 minutes or so, until they begin to soften and take on nice grill marks. Flip. Grill for another 7 minutes. Peaches should be very soft and beginning to ooze their natural juice. If your peaches weren’t very ripe to begin with, you may need to grill longer. Serve with orange honey ricotta (combine fresh ricotta cheese with some orange juice, cinnamon & honey), yogurt or ice cream.