Place poblano peppers directly over a gas flame or under a broiler, turning occasionally until skin is blackened and blistered all over. Transfer to a bowl, cover with plastic wrap, and let steam for 10-15 minutes.

Once cool enough to handle, peel the charred skin off the peppers. Remove the stems and seeds, then give them a rough chop.

In a large pot or Dutch oven, heat olive oil and butter over medium heat. Add the onion and cook until soft, about 5-7 minutes. Add garlic and cook for 1 more minute until fragrant. Stir in cumin, oregano, and coriander and cook for 30 seconds.

Add the chopped roasted poblanos and 2 cups of the chicken broth to the pot. Use an immersion blender to puree the mixture until completely smooth. (Alternatively, blend in a standing blender and return to the pot).

Stir the remaining 2 cups of chicken broth into the pureed base. Bring to a simmer. Reduce heat to low and stir in the heavy cream, shredded chicken, and corn. Heat through for 5-10 minutes, but do not boil. Season with salt and pepper to taste.

Ladle the hot soup into bowls and serve immediately, garnished with desired toppings like cotija cheese, cilantro, and tortilla strips.