Preheat oven to 350°F (175°C),Lightly grease a 9x13 inch baking dish.
In a medium bowl, combine the shredded chicken with 1 ½ cups of the shredded Monterey Jack cheese. Set aside.
In a medium saucepan over medium heat, melt the butter, Whisk in the flour and cook for 1 minute, stirring constantly.
radually whisk in the chicken broth until smooth. Cook, whisking frequently, for 3-5 minutes until the sauce thickens.
Reduce heat to low. Stir in the sour cream, diced green chiles (with their liquid), garlic powder, and cumin. Season with salt and pepper to taste. Do not let the sauce boil.
Spoon about ⅓ cup of the chicken mixture down the center of each tortilla. Roll up and place seam-side down in the prepared baking dish.
Pour the white sauce evenly over the enchiladas. Top with the remaining 1 ½ cups of shredded cheese.
Bake for 20-25 minutes, or until the sauce is bubbly and the cheese is melted and golden. Let stand for 5 minutes before serving.