Preheat your oven to 450°F (232°C). Place the poblano peppers on a baking sheet and roast for about 20 minutes, turning occasionally until the skins are charred and blackened. Once done, cover with foil to steam for 10 minutes, and then peel off the skins, remove the seeds, and chop them into small pieces.

In a large saucepan over medium heat, melt 2 tablespoons of butter. Add ¼ cup of chopped onion and sauté for approximately 5 minutes until it turns translucent. Stir in 2 cloves of minced garlic and 1 teaspoon of ground cumin, allowing them to cook for an additional minute until fragrant. Finally, mix in the chopped roasted poblano peppers.

Pour in 4 cups of chicken bone broth and bring the soup to a rolling boil. Season with salt and pepper to taste, then reduce the heat and let it simmer for 10 minutes. Add 1.5 pounds of boneless, skinless chicken and continue cooking until the chicken is fully cooked through and tender.

Once the chicken is cooked, carefully remove it, and place it in a bowl to cool slightly. In a blender, combine 8 oz of cream cheese, 1.5 cups of shredded cheddar cheese, and 1 cup of warm broth. Blend until smooth and creamy, then return this mixture back to the saucepan, stirring well to combine into the soup.

Preheat your broiler. Portion the creamy Chile Relleno Soup into oven-safe bowls, topping each with 1 slice of cheddar or pepper jack cheese. Place the bowls under the broiler for 2-3 minutes, or until the cheese is melted, bubbly, and slightly golden. Carefully remove from the oven and let cool slightly before serving.