Preheat oven to 350°F. Grease a 12 x 8-inch casserole dish with non-stick cooking spray.
Add cooked shredded chicken, 1 cup cheese, and 1 can of diced chiles to a medium mixing bowl, and stir well to combine. Warm your tortillas slightly in the microwave, wrapped in paper towels for about 30 seconds.
Add about 1/3 cup filling on each tortilla. Roll it up, and place seam side down in the baking dish.
In a small saucepan over medium heat, melt butter. Stir in flour and cook 1 minute. Add broth and whisk until smooth. Heat until thick and bubbly.
Reduce burner heat to low or simmer. Stir in sour cream and heavy cream. Do not bring to boil, you don’t want curdled cream.
Pour the sauce over enchiladas and top with remaining cheese and second can of chiles.
Bake in preheated oven for 20-25 minutes, until the top is bubbly. If needed, place under the broiler for 3 minutes until the cheese is golden.