Preheat pellet grill or smoker to 250 degrees F. Smoke all halved peppers, halved onion, and 2 ears of corn on the grill for 1 hour. Then, allow the vegetables to cool so you can handle them. Dice the smoked peppers and onion, and cut the corn off the cob.
Add 2 tablespoons of butter to a large dutch oven. Saute the smoked vegetables in the pot over medium heat for about 3-4 minutes, or until the onions are tender. Then, add the minced garlic and saute an additional 1-2 minutes.
In a small bowl, mash the drained navy beans with a fork to a slightly chunky consistency. *This will help to thicken the chili. If you have a food processor, you can also blend the beans to a smooth consistency if you wish.
Add the mashed navy beans to the dutch oven with the vegetables. Pour in the other two cans of drained whole beans.
Add the shredded chicken, canned green chiles, chicken stock, and all of the spices to the dutch oven. Stir to combine. Simmer for about 30 minutes over medium-low heat, stirring occasionally.
Add the cream cheese and heavy cream. Stir well, and simmer another 5-10 minutes.
Taste for seasoning and add salt and pepper as needed. Serve with your favorite chili toppings like sour cream, shredded cheddar cheese, sliced green onions, and hot sauce.