Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion and cook for about 5 minutes, until soft. Add the garlic and cook 1 minute.
Stir in the cumin, oregano, chili powder, salt and pepper and cook for 1 minute. Add the green chiles with their liquid.
Add the broth and the whole chicken breasts. Bring to a boil, then reduce to a simmer, cover and cook for 15 to 20 minutes, until the thickest breast reaches 165°F.
Move the chicken to a cutting board and shred it with two forks. While it rests, mash 1 cup of the beans with a fork.
Return the chicken to the pot with all of the beans, whole and mashed. Simmer uncovered for 10 minutes, stirring now and then, until thickened.
Turn the heat to low. Stir in the cream cheese cubes for 2 to 3 minutes, until melted and smooth. Taste, adjust the salt and serve with toppings.