Rinse the peaches and blot them dry with paper towels. Cut each peach in half and discard the pit. Using a pointed chopstick or metal skewer, make a starter hole in the center of each peach quarter, working from the pit side to the skin side. Skewer each peach half with a cinnamon stick.

In a saucepan on high heat, combine the margarine, brown sugar, balsamic vinegar, and cinnamon until thick and syrupy, for approximately 4-5 minutes.

Heat grill to high and oil the grate. Grill peaches for 3-4 minutes per side, until they start to brown and soften a bit. Keep basting the peaches with the balsamic brown sugar syrup. Reserve the remaining syrup.

Stir the minced basil and pistachio nuts into vanilla ice cream and freeze for 24 hours.

Spoon the remainder of syrup over each peach. Add a scoop of ice cream and crushed cookies in the center of the peaches. Serve.