Broil the poblano peppers until well-charred. Let cool, peel off skin, remove seeds, and chop roughly.

Heat the oil in a Dutch oven over medium heat. Sauté celery, carrots, and onion for 5–7 minutes until soft. Add oregano and cook 2 minutes, then stir in garlic until fragrant.

Stir in chopped poblanos and green chiles. Add salt and pepper to taste and cook for 3–4 minutes more. Mix in red chile powder and cumin, then nestle the chicken pieces into the pot.

Pour in enough broth to submerge the chicken. Bring to a boil, then reduce to a gentle simmer and cover. Simmer for about 45 minutes, stirring occasionally.

While the stew simmers, boil the potatoes until just tender. Drain and set aside.

Remove stew from heat briefly. Transfer chicken to a plate to cool for 5–10 minutes, then shred with forks or a mixer. Return shredded chicken to the pot, add cooked potatoes, and gently warm everything together so the potatoes absorb stew flavor without breaking down.

Ladle stew into bowls and garnish with fresh cilantro, chopped onion, sliced jalapeño, or any preferred toppings. Serve with warm tortillas or cornbread for a complete meal.