Put chicken breasts in a large skillet, cover with 3 1/2 cups water, bring to a boil, cover, and simmer 30 minutes.
Remove chicken from the pan, reserving the liquid, let cool, and shred the meat.
In the same pot, heat the oil over medium heat. Add the onion and cook for 10 minutes.
Add the garlic, chiles, cumin, oregano, cloves, and cayenne and cook 2 more minutes.
Add the beans, broth and reserved chicken cooking liquid. Bring to a boil, cover, and simmer, stirring occasionally.
Before serving, add shredded chicken and cheese. Top with additional cheese.