In a saucepan, saute onion in oil until tender. Stir in broth, honey, lime juice, mustard, rosemary, salt and pepper. Combine cornstarch and water until smooth; stir into sauce. Bring to a boil over medium heat. Cook and stir for 2 minutes or until thickened.
Serve with turkey, chicken, fish or pork. Cover and refrigerate leftovers. Yield: about 1-1/2 cups.