Preheat your broiler or light a gas flame. Roast the peppers until their skins blister and blacken, about 5-7 minutes. Seal in a bag for 10 minutes to steam and peel.

In a skillet, heat olive oil over medium heat. Sauté the finely chopped onion for 3-4 minutes until translucent. Add minced garlic and cook for another minute, then toss in the chicken pieces, cooking until no longer pink, about 6-8 minutes.

Once the chicken is cooked through, stir in the roasted and chopped poblano peppers, diced green chilies, sour cream, chicken broth, and flour (if using). Simmer for 3-5 minutes until creamy.

Preheat your oven to 375°F (190°C). Grease a casserole dish and pour the chicken mixture into it. Top with shredded cheddar and Monterey Jack cheese.

Bake for 20-25 minutes, or until the cheese is melted and golden brown. Let it cool for about 5 minutes before serving, and garnish with fresh cilantro.