Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the celery, carrots, onion, and poblano peppers. Sauté for 10-12 minutes until the vegetables are tender.
Stir in the garlic and cook for an additional 30 seconds until fragrant.
Stir in the salt, cumin, oregano, chili powder, and black pepper. Cook for 5 more minutes.
Add the shredded chicken, corn, and broth. Stir, bring to a boil over high heat, reduce the heat to low, cover, and simmer for 15 minutes.
Add heavy cream and shredded cheese. Stir until the cheese has fully melted. Cover and cook for an additional 15 minutes.
Taste for salt and add more if needed. Serve in bowls and topped with lime juice and chopped cilantro.
Notes
Make it mild. Remove the seeds from the poblano peppers to make this soup a mild spice level.
Make it smoky. Roast the poblano peppers beforehand for a smoky flavor. You can also add ½ teaspoon smoked paprika.
Make it vegetarian. You can easily make this soup vegetarian by using vegetable broth, omitting the chicken, and adding veggies like diced bell peppers, potatoes, or broccoli.
Batch it or save leftovers. This soup freezes well for up to 3 months, making it great for batching or just saving for a rainy day. Let the soup cool to room temperature before storing it in freezer bags.