In a small saucepan, heat the water and sugar until the sugar has completely dissolved. Remove from the heat and add the lime juice and rum. Let cool.
Pour into an 8-inch (20 cm) square glass baking dish. Freeze for 6 hours or until the granita is frozen solid.
On a work surface, cut the pineapple in half lengthwise, through the leaves. Using a paring or serrated knife, make a cut between the flesh and the rind, and again between the flesh and the core. Slide the blade under the flesh all the way to the core. Remove the flesh and cut it into cubes. Repeat the steps on the other side. Slice the core into many pieces for easy removal, and discard. Finally, return the cubes of pineapple to each of the emptied halves (see note).
With a fork, scrape the surface of the granita to form crystals. Spread the granita across the pineapple.
Add small scoops of ice cream or sorbet across the pineapple and granita. Garnish with the coconut flakes or mint leaves. Serve immediately.
Click here for a step-by-step tutorial on making a pineapple bowl.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.