Step 1

Roast the poblano peppers until the skin is charred and blistered. You can do this over the open flame on a gas stove, or by heating your broiler to high and placing poblanos within a few inches of the broiler (turning to get all sides charred).

Step 2

Place the peppers in a bowl and cover with plastic wrap. Let cool, then rub the skin to remove as much as possible. Cut out the seeds and then place in a food processor or blender to finely chop. Set aside.

Step 3

In a large saucepan over medium heat, melt the butter. Add the onion and cook, stirring frequently, until translucent, about 5 minutes. Add the garlic, cumin, and poblanos and stir until fragrant, about 1 minute.

Step 4

Stir in the chicken broth and season to taste with salt and pepper. Bring to a boil and then reduce heat to a simmer. Add the chicken pieces and continue to cook until chicken is cooked through, about 10 minutes.

Step 5

Add the cream cheese and the cheddar to the same blend or processor in which you chopped the poblanos. Add about 1 cup of the hot broth from the soup (avoid getting any of the chicken in there). Blend until smooth and then stir back into the soup.

Step 6

To serve: Preheat the broiler. Dish the soup into individual ovenproof bowl and float a slice of cheese on top. Set under the broiler, about 6 inches from the heat and broil until the cheese is melted and bubbly.