Add the black beans and ham to a pot. Add enough water to cover the beans. Simmer, covered with the lid, for 1 1/2 hours to 2 hours or until the beans are tender.
Heat oil over medium-high in a skillet. Add the onion and peppers and saute for 5 minutes until tender. Stir in the minced garlic, cumin, oregano, and saute for 30 seconds.
Add the sofrito and remaining ingredients to the pot. Bring to a boil then turn down to simmer for 30-40 minutes until the beans are creamy. Serve and garnish with toppings.