Preheat grill to medium-high heat.

In a saucepan, melt ¼ cup butter over medium heat. Add brown sugar and cinnamon, and stir until dissolved, about 2 minutes. Add the banana liqueur and dark rum, continue cooking another 2 minutes.

Cut the bananas lengthwise, leaving the peel on. Brush the cut side with melted butter. Arrange the bananas with the cut side down on the grill. Cook until caramelized, about 3 to 4 minutes. Remove from grill, top with ice cream and drizzle with rum sauce.