Preheat the oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish with nonstick cooking spray.
In a medium bowl, whisk together the salsa verde, diced green chiles, sour cream, cumin, garlic powder, onion powder, chili powder (if using), black pepper, and salt until smooth. Pour 1/2 cup of the sauce to the bottom of the baking dish.
In a separate bowl, combine the shredded chicken, softened cream cheese, 1 cup of the shredded Monterey Jack cheese, and about ⅓ cup of the prepared sauce. Mix until well combined.
Warm the tortillas in the microwave or a dry skillet for 10–15 seconds to make them easier to roll.
Divide the chicken mixture evenly among the tortillas. Roll each tortilla tightly and place seam-side down in the prepared baking dish.
Pour the remaining sauce evenly over the enchiladas and sprinkle with the remaining 1 cup Monterey Jack cheese.
Bake for 20–25 minutes, or until heated through and bubbly.
Switch the oven to broil and broil for 2–3 minutes, watching carefully, until the cheese is lightly golden.
Garnish with fresh cilantro and serve warm.