Preheat the broiler to moderate.
Cut the pineapple in half lengthwise.
Scoop out the flesh and cut into small cubes.
Toss the flesh with the rum and return to the shells.
Cover the leaves with foil.
Put the pineapple halves in the broiler pan, sprinkle with the sugar and broil until the sugar has melted.
If the pineapple is too near the heat, the rum may ignite, but the flames will soon subside if the broiler pan is lowered.
Remove the foil and serve at once with the ice cream.