First, gently butter a 9 x 13-inch baking dish and preheat your oven to 350°F. In a large mixing bowl, mix together the shredded rotisserie chicken, softened cream cheese, onion powder, garlic powder, and one cup of Monterey Jack cheese as the oven preheats. Stir until the cream cheese is equally spread and everything is thoroughly mixed.
In a medium saucepan over medium heat, melt the butter. To make a light roux, sprinkle the flour over it when it has melted and whisk constantly for one to two minutes. To let the spices bloom, add the taco seasoning and stir for an additional 30 seconds. To prevent lumps, gradually add the chicken broth while whisking continuously. Simmer the mixture for two to three minutes, or until it slightly thickens. Whisk in the first half cup of Monterey Jack cheese until smooth and melted.
Spoon approximately 1/3 cup of the chicken filling from Step 1 down the middle of each tortilla, working with one at a time, onto a clean surface. Place the enchiladas in your prepared baking dish, seam-side down, and roll them gently but firmly into a single layer. Continue filling and arranging each of the nine tortillas.
After removing the white sauce from the heat in Step 2, allow it to cool for approximately one minute. Gently fold in the green chilies after whisking in the sour cream until smooth and well combined. Make careful to thoroughly coat the rolled tortillas by evenly pouring this creamy sauce over them. For a golden, melty finish, top with the remaining 3/4 cup of Monterey Jack cheese.
Uncover the enchiladas and bake at 350°F for 22 to 25 minutes, or until the filling is well heated and the sauce is bubbling around the edges. Place the baking dish four to six inches away from the broiler element and turn the oven on to broil. Watch carefully as you broil for two to three minutes, or until the cheese on top is golden brown with a few burned places. Before serving, take it out of the oven and give it two to three minutes to rest.