Prepare a charcoal or gas grill with a greased grill rack for direct cooking over medium heat.

Cut unpeeled bananas lengthwise in half; brush cut sides with 1 tablespoon melted butter and sprinkle with 1 tablespoon brown sugar.

Arrange bananas, cut sides down, on grill rack. Grill for 5 to 6 minutes or until peels are dark brown and bananas are softened. Remove from grill; cool slightly. Remove peels from bananas; cut each crosswise in half.

Place a large cast-iron skillet on grill rack to preheat. Remove skillet and add remaining 6 tablespoons butter, maple syrup, and rum. Return skillet to grill. Cook and stir for 4 to 5 minutes or until bubbly. Stir in remaining 1 tablespoon brown sugar until dissolved. Add bananas and cook for 4 minutes more. Remove skillet from grill.

To serve, place 2 banans pieces on each piece of cake; top with a scoop of ice cream and rum sauce.