Build a charcoal fire or preheat a gas grill.
Slice the bananas, in their skins, in half crosswise and then lengthwise so each banana yields 4 pieces. Set aside on a clean platter. In a small bowl, combine the sugar and cinnamon. Drizzle the honey on the cut sides of the bananas and sprinkle them with the cinnamon sugar. Let the bananas sit for 5 minutes.
Place the bananas, cut side down, on the center of grill. Grill for 2 minutes or until grill marks appear. Using a pair of tongs, turn them over and cook for 5 more minutes, or until the skin pulls away from the bananas. Remove the bananas from the grill and serve them immediately, on top of vanilla ice cream and drizzled with bourbon or liqueur, if desired.