Roast the poblano peppers over an open flame or under the broiler, turning occasionally until charred, about 8–10 minutes. Place in a covered bowl to steam for 10 minutes.

In a large pot, heat a splash of oil over medium heat. Add diced onion and minced garlic, sautéing for about 3–4 minutes until softened and fragrant.

Stir in ground cumin and smoked paprika, cooking for an additional 30 seconds to release their aromas.

Add roasted poblano peppers, drained black beans, corn kernels, and diced tomatoes into the pot. Stir until well combined.

Pour in chicken broth and bring to a gentle boil. Reduce heat to low and simmer for 15–20 minutes.

Add shredded cooked chicken and heavy cream, stirring gently to mix. Let simmer for another 5–7 minutes.

Stir in lime juice and chopped cilantro, adjusting seasoning with salt and pepper as needed.

Serve hot, topping with shredded cheddar cheese, sour cream, and extra cilantro if desired.