Preheat oven to 350 degrees F. Grease a casserole dish and set aside.
Melt butter in large skillet over medium heat. Add onion and green chiles and cook until softened, 3-4 minutes.
Add flour and stir to combine. Add chicken broth a little at a time while stirring constantly, until all broth has been added and sauce is smooth. Stir in sour cream. Cook 2-3 until thickened.
In a large bowl add half of the sauce, all of the chicken, and half of the cheese. Working with one tortilla at a time, spread some filling down the center, roll up, and place seam side-down in the casserole dish.
Pour remaining sauce on top of the enchiladas and sprinkle with remaining cheese.
Cover dish with foil and bake for about 20 minutes. Uncover and bake 15-20 minutes more until sauce is bubbling. Serve immediately as desired.
Video
Notes
To make ahead:
Store in the fridge - Prepare as directed and chill for up to 24 hours.
Store in the freezer - Prepare as directed, double wrap, and freeze for up to 2 months. Add 10 minutes of baking time.