Preheat oven to 350 F. Lightly spray a 9x13-inch pan with non-stick cooking spray and set aside.
Melt butter in a large skillet over medium heat. When butter is melted and bubbly, add flour and stir to combine. Continue cooking, whisking continuously until mixture is light golden brown, about 2-3 minutes. Slowly add chicken broth, whisking until smooth. Whisk in garlic powder, onion powder, cumin, coriander, chili powder, and pepper. Bring sauce to a simmer and stir until thickened, 3-4 minutes. Remove from heat and whisk in sour cream and hot sauce. Add salt to taste and set aside.
In a separate mixing bowl, soften cream cheese in microwave until it is easily stirred. Add green chilies and ½ cup of reserved sauce. Stir to combine and add chicken and 2 cups Monterey Jack cheese.
To make the tortillas easier to roll, place between damp paper towels and microwave 15-20 seconds. Place about ⅓-½ cup chicken mixture on each tortilla and roll tightly. Pour 1 cup sauce into bottom of prepared pan and spread evenly. Place tortillas snugly in pan. Pour all remaining sauce on top of the tortillas and top with remaining 2 cups cheese. Bake 30-35 minutes, until hot and bubbly throughout and cheese is melted.