Step 1: Roast poblano peppers over an open flame or under a broiler until charred on all sides. Place in a bowl, cover with plastic wrap, and let steam for 10 minutes.
Step 2: Peel off the charred skins from the peppers, remove stems and seeds, then dice the peppers.
Step 3: In a large pot, heat olive oil over medium heat. Add diced onion and cook until softened, about 5 minutes.
Step 4: Add minced garlic and cook for 1 minute until fragrant.
Step 5: Stir in diced poblano peppers, chicken broth, diced tomatoes, cumin, oregano, salt, and black pepper. Bring to a simmer.
Step 6: Add corn kernels and shredded chicken. Simmer for 15 minutes to allow flavors to meld.
Step 7: Reduce heat to low and stir in shredded Monterey Jack cheese until melted.
Step 8: Stir in chopped cilantro and heavy cream. Heat through for 2-3 minutes without boiling.
Step 9: Taste and adjust seasoning if needed. Serve hot with optional garnishes like tortilla strips or avocado slices.