Roast the poblano peppers under the broiler on a sheet pan until charred, about 8–10 minutes, turning once so the skin blisters evenly. Let them rest until cool enough to handle, then peel, seed, and dice.

Melt the butter in a large pot over medium heat, then sauté the onion for 4 minutes until softened and glossy. Stir in the garlic, cumin, smoked paprika, and chili powder and cook for 2 minutes until fragrant.

Add the chicken broth, corn, and half the diced poblanos, then bring to a simmer. Simmer for 15 minutes, stirring occasionally, until the flavors meld.

Partially blend the soup until thick but still chunky, then stir in the heavy cream. Blend carefully and return to a gentle simmer as needed.

Add the shredded chicken, remaining poblanos, and lime juice, then simmer for 5 minutes until the chicken is hot throughout. The broth should look creamy and lightly speckled with poblano.

Season with salt and black pepper to taste, then turn off the heat. Serve with sour cream, cilantro, green onions, and tortilla strips so each bowl has a visible swirl and topping pile.