Preheat oven to 375°F and lightly grease a baking dish.
Divide shredded chicken and 1 cup cheese evenly among tortillas and roll tightly.
Place rolled tortillas seam-side down in the prepared baking dish.
Melt butter in a saucepan over medium heat.
Whisk in flour and cook for 1 minute until lightly golden.
Gradually whisk in chicken broth and cook until thickened.
Remove from heat and stir in sour cream, green chilies, salt, pepper, and garlic powder.
Pour sauce evenly over enchiladas and top with remaining cheese.
Bake for 20–25 minutes until bubbly and lightly golden.
Garnish with chopped cilantro and serve warm.