Preheat oven to 375°F (190°C) and grease a 9x13-inch baking dish.
In a pan over medium heat, melt butter and whisk in flour. Cook for 1 minute.
Gradually whisk in chicken broth and green enchilada sauce, stirring until the sauce thickens.
Stir in sour cream, diced green chilies, garlic powder, onion powder, cumin, salt, and black pepper.
In a bowl, mix shredded rotisserie chicken with 1/2 cup shredded Monterey Jack cheese.
Divide the chicken mixture evenly among the tortillas, roll them up, and place seam-side down in the baking dish.
Pour the prepared sauce evenly over the rolled enchiladas.
Sprinkle the remaining 1/2 cup cheese over the top.
Bake for 20 minutes until cheese is melted and bubbly.
Garnish with chopped cilantro or diced tomatoes if desired and serve warm.