Cut the bananas in half lengthwise, leaving the peels on. Brush the cut sides of the bananas with oil.
Combine the melted butter with the brown sugar.
Heat a gas or charcoal grill to medium heat. Place the bananas, cut-side down, over direct heat. Close the barbecue lid and grill for 3 minutes. Turn the bananas over, brush with the butter/brown sugar mixture, close the lid, and grill for 5 minutes.
To serve, peel the bananas and serve 2 halves per person with a scoop of ice cream. Garnish with berries and mint sprigs if desired.