Preheat your oven to 425°F (220°C). Place the poblano peppers on a baking sheet and roast for 20-25 minutes until the skin blackens. Remove from the oven and let them cool.
Once cool, peel off the skins, remove seeds, and chop the peppers into small pieces.
In a large pot, heat the olive oil and butter over medium heat. Add the chopped onions, celery, and garlic, cooking until soft.
Add the diced potatoes, ground cumin, and red pepper flakes. Mix well and cook for another 2-3 minutes.
Pour in the chicken broth, bring to a simmer, and then add the chicken chunks. Cook until the chicken is cooked through, about 15 minutes.
Stir in the roasted poblanos and heavy cream, letting it simmer for an additional 5 minutes.
Season with salt and pepper to taste. Lastly, stir in the minced cilantro before serving.
Notes
This soup tastes even better the next day and can be frozen for up to three months.