In a medium bowl, mix rum, brown sugar, vanilla and cinnamon together until sugar is dissolved.
Using a serrated-edged knife, cut out the flesh of the pineapple, leaving a thin border of the skin and cut pineapple flesh into 2-inch chunks.
Place pineapple chunks on grill. Using a pastry brush, baste with rum mixture while grilling and turn occasionally. Grill until golden brown, about 10 minutes.
Add peeled and cut mango chunks into a blender or food processor. Add sugar and lemon juice. Puree until smooth and pour into bowl.
Construct the pirate's treasure by scoping mango ice cream into the hollowed out pineapple bowl, topping with grilled pineapple chunks and mango sauce. Garnish with whipped cream.