Heat oven to 350 Degrees
Fill each tortilla with shredded chicken, and add a tablespoon of cheese
Roll tortillas and put in a baking dish seam side down
Over medium heat, melt butter. Add flour and whisk until thoroughly combined
Add chicken broth, cream of chicken soup, chiles, sour cream, salt, and pepper
Continue to whisk for an additional five minutes, until sauce is heated through and smooth
Pour sauce over enchiladas and sprinkle remaining cheese on top
Bake 25 - 30 minutes