Begin by charring the poblano peppers over an open flame or under a broiler set to high for about 10 minutes. Turn the peppers occasionally until the skins are blistered and blackened. Once done, place them in a bowl and cover tightly with plastic wrap to steam for 10 minutes. After steaming, peel off the skins, remove the seeds, and chop the peppers into small pieces.

In a large saucepan, melt 2 tablespoons of butter over medium heat. Add the chopped onion and sauté for about 5 minutes, or until it becomes translucent. Stir in the minced garlic and ground cumin, cooking for an additional minute until fragrant.

Next, add the chopped roasted poblano peppers to the saucepan. Pour in 4 cups of chicken bone broth, and season the mixture with salt and pepper to taste. Bring everything to a boil over medium-high heat, then reduce the heat to low and let it simmer for about 10 minutes.

Add 1½ pounds of boneless, skinless chicken pieces to the simmering soup. Cook for approximately 10 minutes, stirring occasionally, until the chicken is fully cooked and tender.

In a blender, combine 8 ounces of cream cheese, 1½ cups of shredded cheddar cheese, and 1 cup of the hot broth from the saucepan. Blend until the mixture is completely smooth and creamy. Stir this creamy concoction back into the soup.

Preheat your broiler to high. Divide the soup into 4 ovenproof bowls, and top each with a slice of cheddar or pepper jack cheese. Place the bowls on a baking sheet and broil for about 2-3 minutes until the cheese is melted and bubbly.

Carefully remove the bowls from the oven and let them cool slightly. Serve your comforting Chile Relleno Soup hot.