Prep the oven and pan: Heat oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Cook aromatics: In a skillet over medium heat, sauté the onion in a splash of oil until soft, 4–5 minutes.
Add garlic and cook 30 seconds until fragrant.
Season the chicken: In a bowl, combine shredded chicken, sautéed onion and garlic, green chiles, cumin, chili powder, 1 cup of cheese, 1/4 teaspoon salt, and a few grinds of pepper. Toss to mix.
Make the creamy sauce: In a saucepan, melt butter over medium heat. Whisk in flour and cook 1 minute.
Slowly whisk in chicken broth until smooth. Simmer 2–3 minutes to thicken. Remove from heat, whisk in sour cream, and season with 1/4 teaspoon salt and pepper.
Do not boil after adding sour cream.
Soften tortillas (optional but helpful): Warm tortillas briefly in a dry skillet or microwave under a damp towel so they’re pliable and less likely to tear.
Assemble: Spread 1/2 cup sauce in the baking dish. Spoon about 1/3 to 1/2 cup chicken filling down the center of each tortilla. Roll and place seam-side down in the dish.
Sauce and cheese: Pour remaining sauce evenly over the enchiladas.
Top with the remaining 1 cup cheese.
Bake: Cover loosely with foil and bake 15 minutes. Uncover and bake another 8–10 minutes, until bubbly and lightly golden.
Rest and serve: Let rest 5 minutes. Top with cilantro or green onions and serve with lime wedges if you like.