Roast the poblano peppers over an open flame or a broiler pan for 10-12 minutes until charred and blistered. Cover with plastic wrap to steam for 10 minutes.

Peel the skins off the roasted peppers, discarding any charred parts. Remove the seeds and chop the flesh.

Melt butter in a large saucepan over medium heat. Add chopped onion and sauté for 5 minutes. Stir in minced garlic and ground cumin along with the chopped poblano peppers. Cook for an additional minute.

Pour in chicken bone broth and season with salt and pepper. Bring to a gentle boil, then reduce heat and let simmer. Add chicken pieces and cook for about 10 minutes until no longer pink.

Remove the chicken, let cool slightly, blend with cream cheese, shredded cheddar, and a cup of broth until smooth. Return to the saucepan and mix well.

Ladle soup into ovenproof bowls, top with cheese slices and broil for 2-3 minutes until melted.