3 (15- to 16-ounce) cans great northern beans, undrained
4 cups chicken stock or canned broth
20 ounces shredded Monterey Jack cheese, divided
Sour cream, for garnish
Diced jalapeños, for garnish
Place chicken in a large saucepan; add cold water to cover and bring to a simmer. Cook until no pink remains, 15 to 20 minutes. Drain; when cool enough to handle, cut into 1/2-inch cubes.
In a large soup pot, sauté onions in olive oil over medium heat until translucent, about 8 minutes. Add garlic, cloves, cumin, cayenne and green chiles. Cook, stirring, for 3 minutes. Add chicken, beans and their liquid and chicken stock; bring to a boil.
Add 12 ounces (about 3 cups) of the cheese and simmer for 15 minutes, stirring occasionally.
Serve in bowls topped with remaining cheese; pass sour cream and jalapeños on the side.