To prepare the banana rum, cut the dried banana slices in half and place them in a large canning jar or pitcher with a tight-fitting lid. Add the water, molasses, and brown sugar, stir well, and let sit for 2 minutes.
Stir in the rum. Split the vanilla bean in half lengthwise and scrape out the seeds. Add the seeds and bean to the rum. Shake or stir vigorously to mix all ingredients. Refrigerate for up to 48 hours, stirring or shaking occasionally. After 48 hours at most, strain the rum, discarding the vanilla bean and reserving the bananas for another use (see Bonus from the Bar).
When ready to serve, pour the sugar and coconut into a small bowl and mix together thoroughly. Transfer the coconut sugar to a small plate. Rub the juicy side of the lemon or lime wedge along the outer edge of the lip of each glass–not along the inside of the rim. Holding each glass at an angle, roll the outer edge of the rim in the sugar until it is fully coated.
Fill a pitcher with ice, add the banana rum and pineapple juice, and stir briskly until the pitcher is beaded with sweat and frosty.
Add crushed ice to the prepared coupes. Pour the frappé over the ice, garnish with dried pineapple slices or banana chips, sprinkle with coconut, and serve.
BANANA RUM PUNCH Peel and freeze 4 large, ripe, fresh bananas until firm. Place them in a punch bowl and add the banana rum with the dried bananas, pineapple juice, and 1 liter of pear or apple cider or 1 liter of ginger beer. Sprinkle shredded coconut over the top and serve.