In a mixing bowl, combine the shredded chicken, cream cheese, sour cream, green chiles, and half of the shredded cheese. Mix well.

In a skillet, melt the butter over medium heat. Stir in the flour and cook for 1 minute.

Gradually whisk in the chicken broth, stirring constantly until the sauce thickens.

Remove from heat and stir in the sour cream, garlic powder, onion powder, salt, and pepper.

Preheat the oven to 350°F (175°C).

Spread a small amount of the white sauce in the bottom of a baking dish.

Fill each tortilla with the chicken mixture, roll them up, and place seam-side down in the baking dish.

Pour the remaining white sauce over the enchiladas and sprinkle with the remaining shredded cheese.

Bake in the preheated oven for 25-30 minutes, or until the cheese is bubbly and golden.

Let cool for a few minutes before serving.