Add the 5 cups of broth and chicken to a large pot and bring to a boil. Cook chicken thoroughly. The chicken tenders I used for this recipe only took about ten minutes to cook. If you get a different cut, it may take longer. Chicken should be cooked to an internal temperature of 165 degrees.
Once chicken is cooked, remove from pot and set on a paper towel lined plate to drain. Keep the broth. Skim the white foam off the top.
As the chicken is cooking, dice the poblano and onion. Mince the garlic. Saute poblano and shallots in 1 tbsp of olive oil. Once the poblano and shallots have been sauteing for about a minute, add the minced garlic. Stir the veggie mixture regularly to prevent them from sticking to the pan. After a few minutes, they should be done.
Add the 5 cups of broth to the pot. Add the 1 cup of heavy cream to the broth and stir to incorporate.
Add the shredded chicken, beans, corn, green chilis, and stir to incorporate. Add the 1 tsp lime zest, 2 tsp cumin, 1/2 tsp sumac, 1/2 tsp chili powder, and 1/2 tsp each salt and pepper. Stir to incorporate.
Bring to a boil and boil for 5 minutes. Simmer on medium heat for 20 minutes.