Preheat and prep: Heat your oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish or similar casserole pan.
Sauté the aromatics: Warm olive oil in a large skillet over medium heat. Add onion and bell pepper, and cook 4–5 minutes until softened.
Stir in garlic and cook 30 seconds until fragrant.
Boost the flavor: Add cumin, chili powder, and smoked paprika. Stir for 30 seconds to bloom the spices. Season with a pinch of salt and pepper.
Combine the mix-ins: Stir in the drained tomatoes with green chiles, the extra green chiles if using, corn, and black beans.
Cook 2–3 minutes to warm through.
Make it creamy: Lower the heat and fold in the queso and sour cream. Stir until smooth and evenly combined.
Add chicken and rice: Mix in the cooked chicken and cooked rice, breaking up any clumps. Taste and adjust seasoning with more salt, pepper, or chili powder as needed. The mixture should be creamy but scoopable; if it seems dry, add a splash of chicken broth or milk.
Assemble the casserole: Transfer the mixture to the prepared baking dish and spread it evenly.
Top with the shredded cheese.
Bake: Place in the oven for 18–22 minutes, until the casserole is hot and the cheese is melted and lightly bubbling around the edges.
Finish and serve: Let it rest 5 minutes. Garnish with cilantro and green onions. Serve with lime wedges for brightness.