In a mixing bowl, combine softened cream cheese, shredded chicken, green chiles, 1 cup of Monterey Jack cheese, garlic powder, onion powder, and cumin until well blended.

Spoon the filling evenly into each tortilla, roll tightly, and place seam-side down in a greased 9x13-inch baking dish.

In a saucepan, melt butter over medium heat. Stir in flour and cook for 1 minute to form a roux.

Slowly whisk in chicken broth, bring to a simmer, and cook until thickened, about 3–4 minutes.

Remove from heat and stir in sour cream and remaining green chiles.

Pour the sauce evenly over the enchiladas and sprinkle the remaining 1 cup of cheese on top.

Bake uncovered at 350°F (175°C) for 25 minutes or until bubbly and lightly golden.

Let cool slightly before serving. Garnish with chopped cilantro or green onions if desired.