In a medium-sized saucepan over medium-high heat, add the butter and melt. Whisk in the flour and create a roux. Slowly add in chicken broth and whisk. Add in the diced green chilis, sour cream, and Monterey Jack cheese. Whisk until it starts to thicken and remove from heat.
To Make the Filling:
In a medium-sized bowl combine the chicken, cream cheese, sour cream, green chilies, cumin, and Monterey cheese.
Preheat the oven to 350 degrees. Spray a 9x13 inch dish with cooking spray. Lay a tortilla on a flat surface. Divide the filling evenly and roll the tortilla up and put it in the baking dish. Continue until you have used all of the tortillas.
Pour the sauce on top of the tortillas and sprinkle with cheese. Bake for 25-30 minutes or until heated through and cheese is bubbly. Garnish with cilantro if desired.