01 - Preheat the oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish.
02 - Combine shredded chicken, 1 cup Monterey Jack cheese, 1/2 cup sour cream, green onions, garlic powder, cumin, salt, and black pepper in a bowl. Mix until evenly blended.
03 - Melt unsalted butter in a saucepan over medium heat. Stir in all-purpose flour and cook for 1 to 2 minutes, stirring constantly, until mixture is bubbling but not browned.
04 - Gradually whisk in chicken broth, cooking and stirring for about 3 minutes, until sauce thickens slightly.
05 - Remove saucepan from heat. Whisk in sour cream, diced green chilies, onion powder, and 1/2 teaspoon salt until the sauce is smooth.
06 - Divide chicken mixture evenly among flour tortillas. Roll up each tortilla tightly and arrange, seam-side down, in the greased baking dish.
07 - Pour the prepared white sauce evenly over filled tortillas. Top with the remaining 1 cup shredded Monterey Jack cheese.
08 - Bake uncovered for 25 to 30 minutes, or until cheese is melted, sauce bubbles, and the surface is gently golden.
09 - Allow to cool briefly. Sprinkle with cilantro and additional green onions before serving.