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.

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.

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.

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.

Add the cream cheese and the cheddar to the same blender 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.

Preheat the broiler. Dish the soup into individual ovenproof bowls 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.