Preheat and prep: Heat your oven to 375°F (190°C).
If using a baking dish, lightly grease it or spray with nonstick spray. If using a large oven-safe skillet (10–12 inches), you’ll build everything right in it.
Sauté aromatics: Warm the oil or butter over medium heat. Add onion and cook 3–4 minutes until softened.
Stir in garlic, cumin, chili powder, smoked paprika, salt, and pepper. Cook 30 seconds until fragrant.
Build the creamy sauce: Stir in the green chiles, chicken broth, sour cream (or Greek yogurt), and salsa verde. Simmer gently 2–3 minutes, stirring until smooth and slightly thickened.
Taste and adjust salt. Add lime juice.
Fold in chicken: Stir in the shredded chicken until coated. If using corn, beans, or peppers, fold them in now.
Turn off the heat.
Layer with tortillas: Remove about one-third of the chicken mixture to a bowl. In the pan (or your prepared dish), place a layer of tortillas to cover the bottom, overlapping as needed. Spread half of the remaining chicken mixture over the tortillas.
Sprinkle with about one-third of the cheese.
Repeat layers: Add another layer of tortillas, then the reserved chicken mixture, and another third of the cheese. Finish with a final tortilla layer and the remaining cheese on top.
Bake: Cover loosely with foil and bake 15 minutes. Remove foil and bake another 10–12 minutes until the cheese is melted and the edges are bubbling and lightly golden.
Rest and garnish: Let the casserole rest 8–10 minutes so it sets for clean slices.
Top with chopped cilantro. Add extra lime wedges, sliced jalapeños, or a dollop of sour cream if you like.
Serve: Cut into squares and serve with a crisp side salad, rice, or simply some avocado slices and hot sauce.