In a large mixing bowl, combine shredded chicken and 1 cup of shredded Monterey Jack cheese. Set aside.
Add garlic powder, onion powder, cumin, salt, and pepper to the chicken mixture. Stir to distribute the seasonings evenly.
Lay a tortilla flat and spoon about ¼ cup of the chicken mixture into the center. Roll the tortilla tightly and place it seam-side down in a greased 9×13-inch baking dish.
Continue filling and rolling each tortilla until all are arranged in the dish.
Melt butter in a medium saucepan over medium heat. Stir in the flour and whisk constantly for about 1 minute until it forms a paste.
Gradually whisk in the chicken broth, stirring continuously to prevent lumps. Cook for 3-4 minutes until the sauce thickens.
Remove the pan from heat and stir in the sour cream and diced green chilies until smooth. Taste and adjust seasoning, if needed.
Pour the prepared sour cream sauce evenly over the enchiladas.
Sprinkle the remaining 1 cup of shredded Monterey Jack cheese over the top.
Preheat the oven to 350°F (175°C) and bake uncovered for 20-25 minutes, or until the cheese is melted and bubbly.
Sprinkle with fresh cilantro before serving for added flavor and presentation.
