In a medium saucepan stir together the broth, cornstarch, and pepper; set aside.
Transfer turkey drippings to a gravy separator or a 2 cup glass measuring cup. Pour or skim off the fat. Strain the remaining liquid, if desired. Add 1 cup liquid to the broth mixture in saucepan. Cook and stir over medium heat until thickened and bubbly. Add more broth to desired consistency, if necessary. Keep warm until serving time.