Place the poblano peppers directly over a gas flame or under a broiler. Turn frequently until all sides are blistered and blackened. This gives the soup its smoky signature flavor.

Transfer roasted peppers to a bowl and cover tightly with plastic wrap or a plate. Let them steam for 10 minutes—this softens the skins. Peel off as much skin as possible, then remove stems and seeds. Blend or finely chop the roasted peppers and set aside.

In a large soup pot, melt the butter over medium heat. Add the chopped onions and cook for about 5 minutes until translucent. Stir in the minced garlic, cumin, and chopped poblanos. Cook for another minute until everything is fragrant.

Pour in the chicken bone broth and season with salt and pepper. Stir to combine and bring the mixture to a boil. Then reduce the heat and let it simmer gently.

Add the diced chicken into the simmering broth. Cook uncovered for about 10 minutes, or until the chicken is fully cooked and tender.

In the same blender or food processor used for the poblanos, add cream cheese, shredded cheddar, and about 1 cup of the hot broth from the pot. Blend until smooth and creamy. This ensures the cheese mixture melts evenly into the soup without clumping.

Pour the cheese mixture back into the pot and stir until fully incorporated. The soup should now be rich, creamy, and velvety—just like the inside of a chile relleno.

Preheat your oven’s broiler. Ladle the soup into oven-safe bowls. Top each serving with a slice of cheddar or pepper jack cheese and place under the broiler for 1–2 minutes, until the cheese is bubbly and just starting to brown. Watch carefully to avoid burning.