Preheat your oven to 350°F (175°C) and prepare your baking dish.

In a large bowl, combine the shredded rotisserie chicken, softened cream cheese, garlic powder, onion powder, and 1 cup of shredded Monterey jack cheese. Mix well.

Spoon an adequate amount of the chicken mixture into the center of each flour tortilla and roll them tightly. Place them seam side down in the prepared baking dish.

In a saucepan, melt the butter over medium heat. Add the flour and whisk continuously to create a roux.

Gradually whisk in the chicken broth, ensuring no lumps form. Continue to whisk until the sauce thickens slightly.

Remove from heat and stir in the taco seasoning, sour cream, green chiles, and remaining Monterey jack cheese.

Pour the sauce over the rolled enchiladas, ensuring they are well covered.

Bake in the preheated oven until bubbly and the cheese is slightly browned, about 20-30 minutes.

Remove from the oven and allow to cool slightly before serving.