1. Roast the poblano peppers under a broiler or over an open flame, turning until the skins are charred and blistered on all sides. Transfer to a bowl, cover, and let steam for 10 minutes, then peel, remove seeds and stems, and chop into bite-sized pieces.

2. In a large heavy pot, heat the olive oil and butter over medium heat. Add the diced onion and jalapeño and cook for 4–5 minutes, until softened and fragrant.

3. Stir in the minced garlic and cook for 30 seconds, just until aromatic.

4. Sprinkle the flour over the vegetables and stir to coat, cooking for 1 minute to remove the raw flour taste.

5. Add the cumin, chili powder, smoked paprika, and dried oregano, stirring for another 30 seconds to lightly toast the spices.

6. Slowly pour in the chicken broth while whisking to prevent lumps, then add the chopped roasted poblanos, fire-roasted tomatoes, and corn. Bring to a gentle simmer and cook for 10–15 minutes so the flavors meld.

7. For a creamier texture, use an immersion blender to blend some or all of the soup in the pot, or carefully blend a portion in a regular blender and return it to the pot. Leave some chunks of pepper and corn if you prefer more texture.

8. Reduce the heat to low. Stir in the heavy cream and cubes of cream cheese, whisking until the cream cheese is fully melted and the soup is smooth.

9. Add 1 1/2 cups of the shredded Monterey Jack cheese and stir until melted and creamy. Taste and season with additional salt and black pepper as needed.

10. If you’d like a cheesy crust, ladle the soup into oven-safe bowls, top each with some of the remaining Monterey Jack, and broil for 1–2 minutes until bubbly and golden.

11. Serve the soup hot, topped with chopped fresh cilantro, crushed tortilla chips, and a squeeze of lime juice over each bowl.