Heat the vegetable oil in a large pot or Dutch oven over medium heat. Season the chicken meat with salt and pepper to taste. Stir into the hot oil, and cook until no longer pink in the center, about 8 minutes. Add the onion, jalapeno pepper, and garlic; continue cooking and stirring until the onions are tender, about 3 minutes more. Stir in the cumin, thyme, sage, oregano, allspice, cinnamon, nutmeg, cayenne pepper, salt, and cloves; cook and stir 1 minute.
Pour in the lime juice, chopped green chilies, and chicken broth, then bring to a simmer. Reduce heat to medium-low and cook 45 minutes. Stir in the rinsed white beans, and cook 10 more minutes to reheat. Stir in the Pepper Jack cheese until melted to serve.