Heat 1 tablespoon olive oil in a large pot or Dutch oven and add the onion and peppers. Cook them down for 5 minutes to soften.
Add the garlic, cumin, and salt and pepper, and cook another minute, until you can smell the garlic bloom.
Add chicken, enchilada sauce, tomatoes, corn, black beans, and chicken broth. Stir to incorporate. Bring to a boil, then reduce the heat and simmer at least 20 minutes to cook the chicken and let the flavors develop.
Remove the chicken and shred it with a couple of forks. Return the chicken to the pot and simmer 5 minutes.
Swirl in some lime juice (if desired) then serve in bowls with your other favorite toppings.