01 -
Char the poblano peppers until the skin is blistered and blackened. You can do this directly over a gas flame on your stove, turning with tongs until all sides are charred. Alternatively, place the peppers close to your broiler set on high, turning occasionally until charred all over.
02 -
Place the charred poblanos in a bowl and cover tightly with plastic wrap. The trapped steam will help loosen the skins. Let them cool for about 10 minutes, then rub off as much of the charred skin as possible. Don't worry about getting every bit - a little char adds flavor.
03 -
Cut open the peppers and remove the seeds and membranes. Place the roasted, seeded poblanos in a food processor or blender and pulse until finely chopped but not completely pureed. Set aside.
04 -
In a large saucepan or Dutch oven, melt the butter over medium heat. Add the chopped onion and cook, stirring frequently, until soft and translucent, about 5 minutes. Add the minced garlic, ground cumin, and chopped poblanos. Cook for about 1 minute, just until fragrant.
05 -
Pour in the chicken broth and season with salt and pepper to taste. Bring the mixture to a boil, then reduce the heat to maintain a simmer. Add the diced chicken pieces and cook until the chicken is completely cooked through, about 10 minutes.
06 -
In the same food processor or blender used for the poblanos (no need to clean it), combine the cream cheese and shredded cheddar. Carefully ladle about 1 cup of the hot broth from the soup into the processor, avoiding getting any chicken pieces. Blend until smooth and creamy.
07 -
Pour the cheese mixture back into the soup pot and stir to incorporate completely. Let the soup simmer for another 2-3 minutes to ensure everything is heated through and well combined. Taste and adjust seasoning if needed.
08 -
Preheat your broiler. Ladle the hot soup into individual oven-safe bowls. Float a slice of cheese on top of each bowl. Place the bowls on a baking sheet and set under the broiler, about 6 inches from the heat source. Broil until the cheese is melted, bubbly, and starting to brown in spots, about 2-3 minutes. Watch carefully to prevent burning.
09 -
Carefully remove the hot bowls from under the broiler (they'll be very hot!) and serve immediately. The melted cheese on top will stretch and pull as you eat - just like a real chile relleno!