Combine cider, broth, steak sauce, soy sauce, and pepper.
Reserve 1 1/2 cups mixture in a small saucepan for gravy, set aside.
Use remaining cider mixture for basting turkey breast, set aside.
Place turkey breast on a rack in a roasting pan, insert meat thermometer into meaty portion so that it does not touch bone.
Baste with cider mixture.
Cover and bake at 325° about 1 to 2 hours or until meat thermometer registers 170°, basting frequently with cider mixture.
Let cool 10 to 15 minutes before slicing.
Combine cornstarch with reserved 1 1/2 cups cider mixture in saucepan.
Bring to a boil, and cook 1 minute, stirring constantly, until thickened.
Serve with sliced turkey breast.