Char the poblano peppers over direct heat for about 8 minutes, rotating every 2 minutes, until blackened on all sides.
Seal the hot peppers in a plastic bag and let them steam for 10 minutes to loosen the skin.
Peel, seed, and dice the poblanos into 1/2-inch pieces.
Sauté the diced onion in olive oil over medium heat until soft, then add garlic for 30 seconds.
Season the chicken with cumin, salt, and pepper. Sear in the pot for 3 minutes per side.
Pour in the chicken broth, scraping up browned bits, and bring to a simmer.
Stir in the diced poblanos and any collected juice.
Simmer for about 15 minutes, until chicken reaches 165°F internally.
Blend 2 cups of the soup until smooth, then stir it back into the pot.
Lower the heat and stir in the cream, warming for 2 minutes without boiling.
Taste and adjust seasoning with salt, lime, or extra cumin as needed.
Ladle into bowls, top as desired, and serve hot.