Cut the top and bottom off of the pineapple, peel and cut it crosswise into 8 rings, about 1/2-inch each. Use a spoon or apple corer to carve out the center core of each ring.
Spray a large grill pan with cooking spray and heat over a medium flame. Grill the pineapple, in 2 or 3 batches, for 2 to 3 minutes on each side, until it is nicely brown and grill marks have appeared. (You can also grill this on an outdoor grill sprayed with cooking spray before being heated.)
While the last batch of pineapple cooks, 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 slightly, about 2 minutes. Remove the sauce from the heat.
Place a pineapple ring on each plate, scoop 1/4 cup of ice cream into the center of the ring, and drizzle about 2 teaspoons of sauce on top.