Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking dish with cooking spray.
If you want softer enchiladas, spread a small amount of enchilada sauce on the bottom of the prepared dish; skip this for crisper bottoms.
In a large mixing bowl, combine the softened cream cheese and undrained diced green chiles until smooth.
Stir in the salt and cumin, then add the shredded chicken and mix until the filling is evenly combined.
Spoon about 1/3 cup of the chicken mixture down the center of each tortilla, roll them up, and place seam-side down in the prepared baking dish.
Pour the enchilada sauce evenly over the rolled tortillas, then sprinkle with the shredded cheddar and Monterey Jack cheeses.
Bake uncovered for 20–25 minutes, until the cheese is melted and bubbly. For softer enchiladas, cover and bake 10 minutes, then remove foil and bake an additional 10–15 minutes.
Remove from the oven and serve with desired toppings such as cilantro, sour cream, or avocado.