Peel and cut the plantains into small rounds. Place in a small saucepan and add the cranberry juice, brown sugar and cinnamon stick. Bring to a boil then lower the temperature and let simmer for about 2 hours, stirring every 1/2 hour.
Microwave: Cut off the ends of the unpeeled plantains and place them on a microwave-safe plate. Place a moist paper towel over them and microwave on high for about 8 minutes or until the skin opens up. Let cool and then peel. Slice into small rounds and place in a microwave-safe baking dish. Add the cranberry juice, sugar and cinnamon stick. Microwave on high for 12 minutes.
Serve as a side dish with fresh mint leaves or as a dessert with vanilla ice cream or whip cream.