Preheat your oven to 450°F (230°C). Place the poblano peppers on a baking sheet lined with parchment paper, and roast them for about 20 minutes, turning occasionally until the skins are blistered and charred.

In a large saucepan, melt 2 tablespoons of butter over medium heat. Add ¼ cup of chopped onion and sauté for approximately 5 minutes, until translucent. Add 2 minced garlic cloves and 1 teaspoon of ground cumin; stir for another minute.

Add the chopped roasted poblano peppers to the saucepan, stir well, and cook for an additional 2-3 minutes.

Pour in 4 cups of chicken bone broth, season with salt and pepper, and bring to a rolling boil. Reduce the heat, add 1.5 lbs of cut chicken, and simmer for about 10 minutes.

In a blender, combine 8 oz of cream cheese, 1.5 cups of shredded cheddar cheese, and 1 cup of hot broth. Blend until smooth and stir this back into the soup.

Preheat your broiler to high. Ladle soup into individual oven-safe bowls, top with slices of cheese, and broil for 2-3 minutes.