Preheat broiler and line a shallow baking pan with foil.

Trim pineapple leaves to about 2-inches. Quarter pineapple lengthwise and cut and discard cores. With a sharp knife cut fruit from rinds, keeping rinds intact and reserving them. Cut pineapple crosswise into 1/4-inch thick slices.

In a saucepan cook butter, 4 tablespoons brown sugar, and rum over moderate heat, stirring, 1 minute. Add pineapple, stirring to coat, and cook mixture 1 minute.

Put reserved rinds in baking pan and with a fork and spoon return pineapple pieces to rinds, arranging in original shape. Spoon remaining butter mixture over pineapple and sprinkle tops with remaining 2 tablespoons brown sugar. Broil pineapple about 3-inches from heat until slightly charred and heated through, about 8 minutes. Serve caramelized pineapple with ice cream.