Roast the Poblanos: To get that signature smoky flavor, char the poblano peppers. You can do this easily over an open flame on a gas stove or under a hot broiler, turning them until the skin is blistered all around.
Peel & Chop: Once charred, place the peppers in a bowl and cover with plastic wrap for about 10 minutes to steam. This makes peeling super easy! After they've cooled, rub off the skin, remove the seeds and stems, then finely chop the peppers in a food processor or blender. Set them aside for later.
Sauté Aromatics: In a large saucepan over medium heat, melt the butter. Add the chopped onion and cook for about 5 minutes until it's soft and translucent. Stir in the minced garlic, ground cumin, and your chopped poblanos, cooking for just a minute until everything smells wonderful.
Simmer the Soup: Pour in the chicken bone broth and season generously with salt and pepper. Bring the mixture to a boil, then reduce the heat to a gentle simmer. Add your chicken pieces and continue to cook for about 10 minutes, or until the chicken is fully cooked through and tender.
Creamy Finish: For that rich, creamy texture, add the softened cream cheese and 1 1/2 cups shredded cheddar cheese to the same food processor or blender you used for the peppers. Carefully scoop about 1 cup of the hot broth from the soup into the blender (try to avoid getting chicken pieces in there). Blend until completely smooth and velvety, then stir this cheesy goodness back into your simmering soup.
Serve with Melted Cheese: To serve, preheat your broiler. Ladle the hot soup into individual oven-safe bowls. Float a slice of cheddar or pepper jack cheese on top of each bowl. Place them under the broiler (about 6 inches from the heat) and broil briefly until the cheese is beautifully melted and bubbly. Enjoy this hearty and healthy soup!