Saute the onions and garlic in a dutch oven medium-high heat for around 2 minutes.
Add the rinsed beans and chopped green chiles, then pour in the chicken broth.
Add the sliced jalapenos and season with salt, pepper, and cumin.
Cover, turn the heat to low and cook for 2 hours, until the beans are done. Add the 3 cups of cooked chicken halfway through the cooking time.
Once the beans are done, mix the cornmeal with the milk and add it to the chili.
Cook for 10 more minutes, until thickened.
Adjust the seasoning to taste, adding cayenne pepper and paprika if required.
Add the desired amount of Monterey Jack cheese to the pot and stir until melted.
Serve in a bowl, garnished with cilantro, sour cream and extra cheese, with rolled up warm corn tortillas on the side. Pico de gallo and guacamole also make great accompaniments, if available.