1. Cook rice. Drain and set aside in a bowl.
2. Melt butter in a skillet over medium heat. Add pineapple and mango; sauté 5 minutes until mango and pineapple brown.
3. Add mango pineapple mixture and salt to rice in bowl.
1. Pour beans into a strainer and wash them thoroughly.
2. Place 1-1/2 cups beans in a bowl, with salt, garlic, and cumin, and mash with a fork.
3. Place 1/2 cup remaining beans and egg white in a food processor and process about 20 seconds.
4. Add bean purée to mashed beans in bowl and make sure they are combined well.
5. Add cheese and onion to bean mixture.
6. Shape bean mixture into a 1/2-inch-thick patty.
7. Pour cornmeal in a shallow dish and cover both sides of patties with cornmeal.
8. Heat olive oil in pan over medium heat.
9. Cook patties two at a time, until golden brown, about 2 minutes on each side.
To serve, place rice in the bottom of bowl and serve patty on top.