Prep the oven and pan: Heat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Sauté aromatics: In a skillet over medium heat, warm the oil. Add onion and cook 3–4 minutes until soft.
Stir in garlic for 30 seconds until fragrant.
Season the chicken: In a bowl, combine the shredded chicken with the cooked onion/garlic, 1 cup of the shredded cheese, cumin, chili powder, salt, and pepper. Toss to coat. Taste and adjust seasoning.
Make the sauce base: In a saucepan, melt the butter over medium heat.
Whisk in the flour and cook 1 minute, whisking constantly, to remove the raw flour taste.
Add broth: Slowly whisk in the chicken broth. Bring to a gentle simmer and cook 3–4 minutes until slightly thickened and glossy.
Finish the sauce: Remove from heat. Whisk in sour cream and green chiles until smooth.
Do not boil after adding sour cream to prevent curdling.
Warm the tortillas: Wrap tortillas in a damp paper towel and microwave 30–45 seconds to make them pliable. This prevents cracking when rolling.
Assemble: Spread about 1/2 cup sauce on the bottom of the baking dish. Spoon 1/4–1/3 cup chicken mixture into each tortilla, roll tightly, and place seam-side down in the dish.
Sauce and cheese: Pour the remaining sauce evenly over the enchiladas.
Sprinkle with the remaining cheese.
Bake: Bake uncovered 18–22 minutes, until the cheese is melted and the edges are bubbling. For a golden top, broil 1–2 minutes at the end, watching closely.
Finish and serve: Rest 5 minutes, then top with cilantro and green onions. Serve with lime wedges for brightness.