Dust chicken with oregano, cumin, salt, and pepper. Heat oil in a large skillet over medium-high heat. Add chicken and cook until chicken is browned all over, 4 to 5 minutes, stirring now and then. Add onion, bell pepper and jalapeño pepper, and cook until onion is soft, 4 minutes. Add garlic and cook 1 minute. Transfer to a 4-quart slow cooker.
Puree 1 can of beans with 1 cup of broth in a small food processor or with a stick blender until relatively smooth. Add to slow cooker along with remaining beans and broth. Cover and cook on low for 3 to 3 1/2 hours.
Stir before serving. Sprinkle with cheese.
Tip: For a pretty garnish, swirl in some light sour cream and sprinkle on minced fresh cilantro.