Heat the grill to medium.
Peel the bananas, being careful not to break them. Put the whole bananas on the grill, and cook until grill marks form and the banana is tender but not mushy, about 2 to 3 minutes per side Remove the bananas from the grill to a platter and set aside.
Melt the butter in a large saute pan over low heat. Stir in the sugar, then add the cinnamon, orange juice, and orange zest. Add the banana liqueur and heat through. Stir in the rum and cook until the alcohol burns off, about 2 minutes. Finally, add the grilled bananas and warm them up in the caramel sauce. Arrange the bananas on serving plates and serve with or without ice cream.
You don't want your bananas to be too ripe; otherwise they will fall apart on the grill.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.