Preheat your oven to 450°F (232°C). Place the poblano peppers on a baking sheet and roast them for about 20 minutes, turning occasionally until they are charred and blistered. Once done, remove them from the oven, and let them cool in a covered bowl for 10 minutes. After cooling, peel off the skins, deseed, and chop the peppers into small pieces.

In a large saucepan, melt 2 tablespoons of butter over medium heat. Add 1 chopped onion and sauté for 5–7 minutes until it becomes translucent and fragrant. Stir in 3 minced garlic cloves and 1 teaspoon of ground cumin, cooking for an additional 1–2 minutes, until aromatic.

Add the chopped roasted poblano peppers to the saucepan along with 4 cups of chicken bone broth. Season with salt and pepper to taste. Bring to a boil, then reduce heat to low. Add 1 pound of diced chicken; simmer uncovered for 10 minutes or until chicken is cooked through.

While the soup simmers, blend 8 ounces of cream cheese with 1 cup of the hot soup broth in a blender until smooth and creamy. Return this mixture to the saucepan, stirring until well incorporated.

Preheat your broiler. Ladle the soup into ovenproof bowls, top with cheese slices, and broil for 3–5 minutes until the cheese is melted and bubbly.