Remove 1 chile and 1 teaspoon adobo sauce from can; reserve remaining chiles and sauce for another use. Finely chop chile; set aside.
Heat oil in a large Dutch oven over medium heat. Add chopped chile and sauce, onion, celery, carrot, bell pepper, cumin, and oregano. Cook 7 minutes or until onion is tender, stirring frequently. Add a bit of water if mixture seems dry. When vegetables are tender add garlic and saute for a moment.
Stir in broth; bring to a boil. Add chicken, cover, reduce heat to medium-low, and simmer 25 minutes or until chicken is tender. 15 minutes into cooking time, add potatoes. Remove chicken with a slotted spoon, and cool slightly. Shred chicken with 2 forks and return to pan.
Add hominy (I like a strong hominy flavor and don’t rinse mine, but if in doubt, feel free to do so), bring to a simmer over medium heat. Cook, uncovered, 10 minutes or until potatoes are tender.
Remove from heat and stir in cream, tomato, cilantro, pepper, and salt. Serve with lime wedges.
Keywords: Bargain Meal of the Week, Bell Peppers, Chicken, Chipotle, chowder, Cream, hominy, leftover Chicken, leftover turkey, Leftovers, Lime, Mexican or Southwestern, Poblano Peppers, Soup, Turkey.