For glaze, combine ginger and oil in medium saucepan. Cook over medium heat until ginger begins to brown. Stir in soy sauce, brown sugar and rum. Bring to boil; remove from heat.
For turkey, remove giblets and neck from turkey. Place giblets and neck in medium saucepan and add enough water to cover; bring to boil. Continue to boil 20 minutes; remove from heat. Cover saucepan, cool 10 minutes and refrigerate.
Preheat oven to 350°. Rinse turkey and pat dry with paper towels. Rub turkey with oil. Liberally salt and pepper turkey inside and out. Tie ends of legs to tail with kitchen twine; lift wing tips up and over back so they are tucked under bird. Place in large roasting pan with breast side up. Insert meat thermometer into thickest part of thigh without touching bone. Pour 1 cup water into pan. Brush glaze on turkey. Loosely cover with aluminum foil and roast 3 to 3 1/2 hours, basting with glaze every 30 minutes.
To test for doneness, meat thermometer should register 180° and juices run clear when thickest part of thigh is pierced with fork. Transfer turkey to serving platter and let stand 20 minutes before carving. Reserve remaining glaze and 1 cup drippings from roasting pan for gravy.
For gravy, dissolve cornstarch in water in small bowl. Pour remaining glaze and reserved drippings into saucepan containing giblet mixture. Bring to boil over medium heat. Remove neck and giblets. Stirring constantly, add cornstarch mixture and continue to cook 5 to 8 minutes or until gravy thickens. Serve with turkey.