Preheat oven to 350°F and grease a 9×13-inch baking dish. Mix shredded chicken with 1 cup cheese. Fill tortillas with the mixture, roll tightly, and place seam-side down in baking dish. Melt butter in a saucepan, whisk in flour, and cook 1 minute. Slowly whisk in chicken broth until thickened. Remove from heat and stir in sour cream, green chilies, garlic powder, salt, and pepper. Pour sauce over enchiladas and sprinkle remaining cheese on top. Bake 20–25 minutes until bubbly and lightly golden. Garnish with cilantro before serving.
Notes
Use rotisserie chicken for convenience. Do not boil the sauce after adding sour cream to prevent curdling.