Using a long sharp knife, cut the pineapple in half lengthwise, starting at the fruit end and cutting through the leaves as well as the fruit. Cut the core out of each pineapple half and cut out the flesh; a grapefruit knife works well for this. Be careful not to pierce the shell.
Cut the pineapple flesh into 1-inch dice and transfer to a mixing bowl. Stir in the ice cream and 2 tablespoons rum (if using). Pack this mixture back into the pineapple shells while you prepare the meringue.
To make the meringue, place the egg whites and cream of tartar in the bowl of a standing mixer and start beating at low speed. Gradually increase the speed to medium and beat until frothy; keep the mixer at this speed while you cook the sugar.
Place 1/2 cup of the sugar in a saucepan with 3 tablespoons water. Cover the pan and bring to a boil. Uncover the pan and cook the sugar to the soft ball stage, (239°F); the mixture will look thick and sticky.
When the sugar is cooked, remove the pan from the heat. Increase the mixer speed to high and beat the eggs whites to soft peaks. Add the remaining 1/4 cup sugar and beat until the whites are glossy and firm; this will take about 8 minutes in all. With the mixer on, beat the hot sugar mixture and vanilla into the egg whites and continue beating until cool.
Transfer the meringue to a piping bag fitted with a large star tip. Pipe decorative swirls of meringue over the top of the stuffed pineapple halves to completely encase the fruit and ice cream. If you don't have a piping bag, spread the meringue over the fruit with a spatula. Freeze for at least 30 minutes to firm up the ice cream. (You can also assemble it ahead and freeze it solid, in which case remove it from the freezer 30 minutes ahead of time to thaw at room temperature.)
Set up your grill for indirect grilling and preheat to high (at least 450°). Place the pineapple on the grill grate away from the heat. Indirect grill until the meringue is handsomely browned, 3 to 6 minutes. Transfer the baked Hawaii to a heatproof platter. If you choose to flambée the dessert, warm the remaining 1/4 cup of rum in a small saucepan, but do not let it boil. Carefully ignite the rum with match or lighter and pour it over the dessert. Serve at once.