Bring sugar, water and cinnamon stick to a boil and let them continue
to boil for about 20 minutes. You should now have about 2 1/2 to
3 cups liquid. Remove the cinnamon stick.
Clean and dice the pineapple and bananas and blend it with the syrup
to a coarse puree. Pour the mixture into a shallow ovenproof dish
and add cinnamon, lime peel and juice. Set the dish in the oven
and let the fruit puree cook for about 5 to 6 hours. The cooking
time will depend upon the depth of the mixture in the dish. From
time to time, scrape the mixture from the sides of the dish and
stir it well. This is very important toward the end of the cooking period.
When the mixture is rich, dark brown, thick and sticky, transfer
it to a small serving dish and glaze it quickly under the broiler. Set it aside to cool.