Pour the pineapple juice into a medium bowl. In a 3-qt. nonreactive saucepan, combine 1 cup of the coconut milk with the sugar. Bring to a boil, stirring to be sure the sugar is incorporated. Boil until reduced by half, about 5 minutes. Add the remaining coconut milk and boil for another 5 minutes; the mixture will turn a brownish color. Whisk the mixture into the pineapple juice and then add the dark rum. Chill, stirring occasionally, and then freeze in an ice-cream machine according to the manufacturers directions.

If you dont have an ice-cream machine, you can make a granita, which will have a coarser texture but will still be refreshing and delicious. Simply freeze the mixture in the freezer, stirring it vigorously with a fork every half hour or so for a few hours, to ensure that the coconut syrup doesnt separate.

Serving size = 1 cup