Rummy Pineapple with Vanilla Ice Cream

1 ripe medium pineapple, peeled,
    cored, and sliced into eight 1-inch rings
6 tablespoons unsalted butter, cut into tablespoons
1/2 cup plus 1 tablespoon light brown sugar
1/4 cup white rum
8 scoops vanilla ice cream

Cut slits halfway into the pineapple rings at 1-inch intervals, leaving the rings attached at the center. Scatter the butter over the bottom of a large skillet, preferably nonstick. Sprinkle 1/2 cup of the brown sugar evenly over the butter and place a single layer of pineapple slices on top. Cook over moderate heat for 5 minutes after the butter and sugar begin to bubble. Turn and cook for 5 minutes longer. Transfer the rings to a platter. Add remaining slices to the skillet and cook in the same manner; transfer to the platter.

Pour the accumulated juices from the platter back into the skillet and add the remaining 1 tablespoon brown sugar. Bring to a boil over high heat and cook until the liquid is reduced to a syrupy caramel, 3 to 5 minutes. Remove from the heat and let cool to lukewarm. Stir in the rum.

To serve, place a pineapple ring in each of 8 dessert dishes. Top each with a scoop of vanilla ice cream and spoon the sauce over all, dividing evenly.