Pineapple-Banana Dessert

1 1/2 cups brown sugar
4 cups water
1 (2-inch) cinnamon stick
1 (3 1/2 pound) pineapple
2 pounds bananas
2 (1-inch) cinnamon sticks
Juice and peel of 1/2 Mexican lime

Preheat oven to 325 degrees F. 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 pur