In a medium saucepan, melt butter over medium heat. Once melted, whisk in all-purpose flour and cook until golden and bubbling. Gradually pour in chicken broth while whisking continuously until thickened. Remove from heat and stir in sour cream, cumin, salt, and pepper. Set aside.

In a large mixing bowl, combine cooked shredded chicken, diced onion, diced green chiles, chopped cilantro, and Monterey Jack cheese. Stir until well combined.

Preheat oven to 350°F (175°C). Spread a thin layer of the white sauce on the bottom of a greased baking dish. Fill tortillas with the chicken mixture, rolling tightly and placing seam-side down in the dish.

Pour the remaining white sauce evenly over the tortillas and sprinkle with shredded cheddar cheese.

Bake uncovered for about 25-30 minutes until bubbly and cheese is golden brown. Allow to rest for 5 minutes before serving.