Melt 4 tbsp. butter in a saucepan over medium heat.
Then add 4 tbsp. flour, stirring constantly.
Once the flour and butter have mixed together and are starting to brown a bit, slowly add the 2 cups of chicken broth, while continuing to stir. Reduce the heat if it starts to bubble too much and continue to cook until the sauce begins to thicken. Once the sauce is thick enough, remove it from the heat and let it cool while you work on the other parts of the dish.
Stir together the taco seasoning with the cooked, shredded chicken (you can use my homemade taco seasoning recipe and also check out how to make Instant Pot shredded chicken).
Put the green chiles and the sour cream in a large bowl, then add the cooled roux (butter/flour/chicken broth mixture).
Then add a big dollop of the sauce to the cooked chicken and taco seasoning.
Line up the ingredients for making the enchiladas: Tortillas, chicken, cheese, and sauce.
For each enchilada, put about ½ cup of chicken and ¼ cup of cheese down the center of each tortilla, then roll it up and put it in a 9x13 pan. Do this until you have 8 large enchiladas.
Top the enchiladas with the sauce and then sprinkle the rest of the cheese on top.
If you want, you can also sprinkle parsley or cillantro over the top for some color and a bit of added flavor.
Bake in a preheated oven at 400 degrees for about 20 minutes.