Preheat your oven to 425°F (220°C). Arrange whole poblano peppers on a baking sheet and roast for about 20 minutes, turning them halfway through cooking until they're nicely charred and blistered. Cover with foil or a kitchen towel for 10 minutes to steam; peel, seed, and chop after cooling.

In a large pot or Dutch oven, heat 2 tablespoons of olive oil over medium heat. Add diced yellow onion and sauté for about 5 minutes until translucent. Stir in minced garlic and cook for an additional minute until fragrant.

Stir in the chopped roasted poblano peppers and 2 cups of shredded chicken into the pot, mixing them with the sautéed onions and garlic for about 2 minutes. Pour in 4 cups of chicken broth and bring to a gentle boil.

Once boiling, reduce the heat to low and stir in 1 cup of heavy cream. Allow to simmer uncovered for about 10 minutes.

Remove from heat and stir in lime juice. Taste and add salt and pepper as needed.

Ladle soup into bowls and garnish with chopped cilantro and optional red chili or jalapeño slices. Serve immediately with warm tortillas or crusty bread.