Preheat oven to 350°F (175°C) and lightly grease a 9x13 inch baking dish.

In a medium saucepan over medium heat, melt butter and whisk in flour for 1-2 minutes to create a roux without browning.

Gradually whisk in the chicken broth and cook until the mixture thickens into a smooth sauce.

Remove the saucepan from heat; whisk in the Greek yogurt, diced green chiles, garlic powder, onion powder, salt, and pepper until fully incorporated.

In a large mixing bowl, combine the shredded chicken with 0.5 cup of the prepared white sauce.

Briefly warm tortillas in a microwave for 30 seconds to ensure they are pliable.

Fill each tortilla with approximately 2 oz of the chicken mixture, roll tightly, and place seam-side down in the baking dish.

Pour the remaining white sauce evenly over the tortillas and top with the shredded Monterey Jack cheese.

Bake for 25 to 30 minutes until the sauce is bubbling and the cheese is lightly golden.

Garnish with fresh cilantro and let rest for 5 minutes before serving.