Roast the poblanos: Set your oven to broil and place the poblanos on a foil-lined sheet. Broil 6–8 minutes per side until blackened and blistered. You can also char them over a gas flame or on a grill.
Steam and peel: Transfer hot poblanos to a bowl, cover with a plate or plastic wrap, and let steam for 10 minutes.
Peel off the skins, remove stems and seeds, and slice into strips or chop.
Preheat the oven: Reduce heat to 375°F (190°C). Grease a 9x13-inch casserole dish.
Sauté the aromatics: In a large skillet, heat olive oil over medium. Add onion and cook until translucent, 4–5 minutes.
Stir in garlic, cumin, smoked paprika, and oregano; cook 30 seconds until fragrant.
Build the filling: Add green chiles and corn to the skillet. Stir in cream cheese until it melts and turns creamy. Pour in chicken broth and sour cream, stirring until smooth.
Season with salt and pepper.
Add the chicken and poblanos: Stir in shredded chicken and the roasted poblano strips. Fold in 1 cup of shredded cheese until everything is well mixed.
Adjust and brighten: Taste and adjust seasoning. Add lime juice and cilantro if using for freshness.
Assemble: Spread the mixture evenly in the prepared baking dish.
Top with the remaining 1 cup of shredded cheese.
Bake: Bake uncovered for 18–22 minutes, or until bubbly around the edges and the cheese is fully melted and lightly golden.
Rest and serve: Let the casserole rest for 5–10 minutes before serving so it sets. Garnish with green onions, cilantro, or your favorite toppings.