Brush a very light layer of olive oil on each side of the cut side of each peach half.
Put the peaches face down on the grill and brush the skin side with olive oil.
Grill peaches 4 to 5 minutes, undisturbed, until there are distinct grill marks on the peaches.
Flip the peaches and allow then to grill on the skin side until they are charred, warmed through and tender, but not mushy. 4-5 minutes.
As Dessert: remove peaches to individual bowls and top with ice cream or a big dollop of whipped cream. Drizzle balsamic vinegar of choice over the peaches and ice cream and serve. Pass a pitcher with additional balsamic vinegar (eat without ice cream for less sugar)