Melt butter with brown sugar in a small pot over medium-low heat
Add bourbon and simmer until reduced by half and thickened
Preheat BBQ to 375°F
Brush cut side lightly with vegetable oil
Place peaches cut side down over hot grills in BBQ
Grill for 3-5 minutes, until grill marks are deep brown and peaches start to soften
Turn peaches over, peel side down, and brush bourbon sauce lightly onto cut side.
Close lid and allow to grill for additional 3-5 minutes
Remove to plate and pour remaining bourbon sauce over the peaches. Or place peaches on top of bowls of ice cream and pour sauce over the peaches and ice cream