Combine the egg and milk; stir in bread crumbs, onion, and pepper.
Add ham; mix well.
Shape mixture into four 4-inch patties.
In saucepan combine brown sugar, honey, dry mustard, and the spiced apple syrup; heat through.
Grill patties over medium-hot coals for 5 minutes.
Turn; brush with glaze.
Place an apple ring atop each patty; brush with glaze.
Grill ham patties till done, 5 to 6 minutes more.
Pass remaining glaze with patties.