Preheat oven to 400ºF.
Place whole poblano peppers on a baking sheet (line with foil for easy clean-up) and roast for 35-40 minutes or until skins are blackened, flipping once.
Place peppers in a plastic bag, or a bowl covered with plastic wrap, and let cool for 10-15 minutes.
In a large pot, heat oil over medium heat. Add chicken, onion, salt, and black pepper and cook 5-6 minutes, stirring frequently, or until onions are translucent.
Add garlic and cumin and cook for one minute, stirring, until fragrant.
Add flour and cook, stirring constantly, for 2 minutes.
Add chicken broth and bring to a simmer.
Once chiles have cooled, remove skin, stem, and seeds. Dice the flesh of the peppers and add to soup.
Simmer for 20-30 minutes. Reduce heat to low and stir in cream cheese and cilantro, stirring to melt cream cheese.
Serve topped with cilantro and cheddar cheese.