Heat the oil in a large pot over medium heat. Stir in the onion, bell pepper, carrot, and garlic, and cook 5 minutes, until tender. Mix in 1 can black beans and chicken broth.
In a blender, puree remaining can of beans until smooth. Mix into the pot. Bring soup to a boil. Reduce heat to low. Mix in ham, cumin, salt, and pepper. Simmer 20 minutes. Garnish with Cheddar cheese and sour cream to serve.