Preheat oven to 175 degrees Celsius (350 degrees Fahrenheit) and lightly coat a 9x13 inch baking dish with non-stick spray.
In a medium saucepan over medium heat, melt the butter and whisk in the flour, cooking for 60 to 90 seconds to remove the raw flour taste.
Slowly whisk in the chicken broth, stirring constantly until the mixture thickens into a smooth gravy.
Remove the saucepan from the heat and allow to cool slightly for 2 minutes before whisking in the Greek yogurt, green chiles, garlic powder, onion powder, cumin, salt, and pepper.
Combine the shredded chicken with 240ml (1 cup) of the yogurt sauce in a large mixing bowl.
Distribute the chicken mixture evenly among the 12 tortillas, roll them tightly, and arrange them seam-side down in the prepared baking dish.
Pour the remaining white sauce over the top of the tortillas, ensuring the edges are covered to prevent drying.
Top evenly with the shredded Monterey Jack cheese.
Bake for 25 to 30 minutes until the sauce is bubbling and the cheese has melted and lightly browned.
Allow to rest for 5 minutes before garnishing with chopped cilantro and serving.