#### Prepare the Filling:
In a large bowl, combine shredded chicken, 1 cup of Monterey Jack cheese, sour cream, and cilantro (if using). Mix well.
#### Assemble the Enchiladas:
Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish.
Place a generous scoop of the filling in the center of each tortilla. Roll them up tightly and place seam-side down in the prepared baking dish.
#### Make the Sauce:
In a medium saucepan, melt the butter over medium heat. Add the flour and whisk constantly for 1–2 minutes to form a roux.
Gradually pour in the chicken broth while whisking to prevent lumps. Cook for 3–4 minutes until thickened.
Remove the saucepan from heat and stir in sour cream, shredded cheese, and green chilies. Season with salt and pepper to taste.
#### Bake the Enchiladas:
Pour the creamy sauce evenly over the enchiladas, ensuring all are well coated.
Sprinkle the remaining 1/2 cup of cheese over the top.
Bake for 20–25 minutes, or until the cheese is melted and bubbly. For a golden finish, broil for 1–2 minutes.