To a large shallow bowl, add enchilada sauce. Using tongs, carefully dip a tortilla (that was just dipped in warm oil) in the enchilada sauce.
Be careful not to press the tongs too tight so not to tear the tortilla.
Cover the entire tortilla with sauce. Place the tortilla dipped in enchilada sauce onto a large plate.
After adding a thin layer of sauce to the casserole dish, and dipping the tortillas in the sauce, there should be just under 2 cups of sauce left in reserve.
To the middle of the tortilla, add a "row" of shredded Monterey jack cheese about 1/2-inch from the left and right edges of the tortilla.
Top the cheese with shredded chicken, cheddar cheese and diced green onion.
Carefully roll the tortilla as tight as possible. Lay the enchilada, seam-side-down, in the casserole dish. Repeat the process for the remaining tortillas.
To prevent the enchiladas from sticking to one another or to the dish, when placing the remaining enchiladas in the casserole dish, leave some space in between each enchilada, and also in between the enchiladas and the sides of the dish.
Using a large spoon or ladle, top the enchiladas with 2/3's cup of the remaining enchilada sauce (reserve 1-1/3 cups of sauce for serving).
Top the enchiladas with a layer of the remaining cheddar cheese, Monterey jack cheese and diced green onions.
Cover the enchiladas with foil. Keep the foil away from the enchiladas (don't let the foil touch the enchiladas) so that the cheese doesn't stick to the foil.
Bake the covered enchiladas in a preheated oven until they're warmed through (about 8 minutes).
Then remove the foil and let bake until the cheese on top of the enchiladas melts (about 10 minutes).