Preheat the oven to 425ºF. Spray a 9x13-inch baking dish with nonstick cooking spray.
Combine 1 cup of the cheese and the chicken. Place some of the mixture down the center of each tortilla and roll up, placing in the prepared dish, seam side down.
Melt the butter in a skillet over medium heat. Stir in the flour and cook for 1 minute. Slowly whisk in the chicken broth. Cook the mixture until thickened. Stir in the sour cream and the green chiles. Season to taste with salt and pepper. Pour the mixture over the top of the enchiladas. Sprinkle the remaining cheese over the top.
Bake in the preheated oven for 20 to 25 minutes, or until the cheese is melted and bubbly. Sprinkle with cilantro before serving, if desired.
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Notes
Nutrition information provided as an estimate only. Various brands and products can change the counts. Any nutritional information should be used as a general guide.