Use a spoon or apple corer to carve out the center core of each ring.
Grill the pineapple for 2-3 minutes on each side, or until it is nicely brown and grill marks have appeared.
While the pineapple cooks, heat the butter, sugar, and rum in a small saucepan over a low heat.
Continue to stir the mixture until the sugar dissolves (about 2 minutes), and the sauce has thickened slightly. Remove the sauce from the heat.
Place a pineapple ring on each plate and scoop 1/4 cup of ice cream into the center of the ring.
Drizzle about 2 teaspoons of sauce on top. Enjoy!