Roast the poblano peppers directly over a gas flame or under a broiler until the skin is blackened on all sides. Place them in a bowl, cover tightly with plastic wrap, and let them steam for 10 minutes. Peel off the skin, remove the seeds and stems, and roughly chop the flesh.
Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion and cook until softened, about 5 minutes.
Add the minced garlic, cumin, and oregano. Cook for 1 minute until fragrant.
Add the roasted poblano peppers and chicken broth to the pot. Bring the mixture to a simmer.
Stir in the shredded chicken and rinsed black beans. Simmer for 10 minutes to allow flavors to meld.
Reduce the heat to low. Stir in the heavy cream. Heat through gently, but do not boil after adding the cream.
If using, stir in the shredded cheese until melted and smooth. Season with salt and pepper to your taste.
Serve hot, topped with your preferred garnishes.
Notes
To make this recipe gluten free, confirm your chicken broth is certified gluten free.
For a lighter version, substitute evaporated milk for heavy cream.
Roast the peppers ahead of time to save time on a busy evening.
This soup freezes well before adding the cream; add the cream when reheating.