Roast poblanos over a gas flame or under the broiler until blistered, about 5-7 minutes. Steam in a bowl covered with plastic wrap for 10 minutes, then peel and chop.

In a large saucepan, melt butter over medium heat. Add diced onion and sauté for about 5 minutes until translucent. Mix in minced garlic and ground cumin for another minute.

Stir in roasted poblanos and chicken bone broth, season with salt and pepper. Bring to a boil, then let it simmer for 10 minutes.

Add bite-sized chicken pieces and cook for about 10 minutes until fully cooked and tender.

Blend cream cheese and shredded cheddar with a cup of the hot broth until smooth, then stir back into the soup, mixing well.

Ladle soup into oven-safe bowls, top with more cheddar, and broil for 2-4 minutes until cheese is bubbly and golden.