Cut the top and bottom off of the pineapple, peel and cut it into 1/2-inch round slices. Use a spoon or apple corer to carve out the center core of each ring.
Spray a grill or grill pan with nonstick spray, heat on medium heat. Once hot, grill the pineapple for 2 to 3 minutes on each side, until it is nicely brown and grill marks have appeared.
In the meantime heat the butter, sugar and rum in a small saucepan over a low heat, stirring, until the sugar is dissolved and the sauce has thickened, about 2 - 4 minutes. Remove the sauce from the heat.
Place a grilled pineapple ring on the plate, scoop ice cream into the center of the ring, and drizzle the sauce on top.