About 1.5 hours before serving:Sprinkle roast with half tsp. salt and quarter tsp. pepper.Place boneless beef rib eye roast,fat side up,on rack in open roasting pan.Insert meat thermometer so bulb is centered in thickest part,but not resting in fat.Do not add water.Do not cover. Roast in 350 degree oven to desired degree of doneness.Allow 18 to 20 minutes for rare;20 to 22 minutes for medium. About 15 minutes before serving,remove roast when meat thermometer registers 60ºC or rare;155 degrees for medium.Tent with aluminum foil;allow roast to "stand" 15 minutes in warm place before carving. Roast should continue to rise about 5 degrees in temperature to 60ºC or rare,160 degrees for medium. While roast is standing,remove rack from roasting pan;skim fat.Add onions to pan drippings;place roasting pan over medium high heat on top of range.Cook onions,stirring occasionally,until tender,about 3 minutes.Add wine;bring to boil;cook about 3 minutes or until thickened. Combine cornstarch and remaining,salt and pepper.Gradually,add beef broth to cornstarch mixture,stirring constantly;add to wine mixture in roasting pan.Continue cooking.Stir in mushrooms and parsley.Pour into serving container.Carve rib eye roast into thin slices.Serve with Red Wine and Mushroom Sauce.