Preheat oven to 350 degrees F. with a rack in the middle of the oven. Spray a 9x13 casserole dish with non-stick spray.
In a large saute pan over medium heat, cook onion and sweet pepper in 2 tablespoons of butter until opaque (about 5-7 minutes).
While the vegetables are cooking, put the chopped chicken and chopped green chilies into a large bowl. Add the onions and peppers once cooked and stir to combine.
In the now empty sauté pan, melt the 3 remaining tablespoons of butter over medium heat. Stir in the flour, coriander and salt to combine. Whisk in the chicken broth all at once. Cook and stir until thickened and bubbly, about 3-5 minutes. Keep at a bubble for 1-2 minutes longer.
Remove the pan from the heat and add the sour cream and ¾ of the shredded Monterey Jack to the sauce, stirring well to combine. Taste and add salt if it needs it.
Stir one cup of the sauce into the chicken and vegetable mixture. Pour ½ cup of the sauce in the bottom of the casserole pan and swirl to thinly coat the bottom.
Fill each tortilla with 1/3 to ½ cup of the filling, roll up, and lay in the casserole pan snugly together.
Pour the remaining sauce over the filled tortillas in the pan and smooth with a spoon. Sprinkle the top with the remaining Monterey Jack.
Bake, uncovered, for about 25 minutes or until bubbly and tips of the tortillas are just starting to get very lightly browned.