Preheat oven to broil and move one of the oven racks to the top portion of the oven. Line a sheet pan with foil and place the poblanos, jalapeño, onion, tomatillos, and garlic cloves on it. Drizzle with a tablespoon of olive oil and rub everything until it's coated. Sprinkle with salt and pepper.

Broil for 6 minutes and then rotate the sheet pan and broil another 6 minutes or until the chile skins are blackened and the tomatillos have softened. Remove from the oven and roughly chop the poblanos, jalapeño, and onion.

Add all of the vegetables along with any of the juices from the tomatillos to a food processor or blender. Add in the dried spices, can of diced green chiles, cilantro, lime juice, and chicken broth or water. Purée until smooth and taste for seasoning. Add additional salt, pepper, or lime juice as needed.

Add the remaining tablespoon of olive oil to a large skillet. Heat over medium-high and swirl the oil to coat the bottom of the pan. Add in the chicken and spread it into a single layer. Season with salt and pepper and let it cook undisturbed for about 3 minutes.

Once browned stir it and cook for another minute. The chicken shouldn't be fully cooked at this point. Pour in the chile verde sauce and stir. Cover with a lid and simmer on low for 15 minutes.

Serve the chicken chile verde over rice or with warm tortillas. Top with crumbled queso fresco and chopped cilantro if desired.