Melt 4 tablespoons of butter in a large saucepan over medium heat. Whisk in ¼ cup of all-purpose flour to create a roux, cooking for about 1 minute until light golden. Gradually add 2 cups of chicken broth while whisking continuously, letting thicken for 3-4 minutes until coats back of spoon. Remove from heat and stir in 1 cup sour cream, 1 teaspoon ground cumin, and season with salt and pepper.

In a large bowl, combine 2 cups cooked shredded chicken, ½ cup diced onion, 1 can diced green chiles, and ¼ cup chopped cilantro. Add 1 cup prepared white sauce and 1 cup cheese mixture. Stir until chicken is coated and combined.

Preheat oven to 350°F (175°C). Grease a 9x13 inch baking dish lightly.

Spread a thin layer of white sauce on bottom of greased baking dish. Fill each flour tortilla with about ¼ cup chicken mixture, rolling tightly and placing seam-side down in dish.

Pour remaining white sauce over rolled enchiladas, covering completely. Sprinkle remaining cheese mixture on top.

Bake uncovered for 25-30 minutes, until top is bubbly and golden brown.

Remove from oven and allow to cool for about 5 minutes before serving.