Preheat the oven to 375°F (190°C). Grease a 9×13-inch baking dish.

Fill the tortillas: Divide the shredded chicken and Monterey Jack cheese evenly among the tortillas. Roll them up tightly and place them seam-side down in the prepared baking dish.

Make the sauce: In a saucepan over medium heat, melt the butter. Stir in the flour and cook for 1 minute until slightly golden. Slowly whisk in the chicken broth and cook until thickened, about 3-4 minutes.

Stir in the sour cream, diced green chilies, garlic powder, onion powder, salt, and black pepper. Cook for another 2 minutes, stirring continuously, but do not let it boil.

Pour the sauce evenly over the enchiladas, then sprinkle shredded cheddar cheese on top.

Bake uncovered for 20-25 minutes, or until the cheese is melted and bubbly.

Garnish with fresh cilantro if desired, and serve warm.