Combine ham, breadcrumbs, milk, mustard, pepper, and beaten egg in a small mixing bowl; stir until well blended. Cover with plastic wrap, and chill 15 minutes. Pat ham mixture evenly around each hard cooked egg. Cover with plastic wrap, and chill 1 hour.
Using a frying basket, fry 2 eggs at a time in deep, hot oil (350°) for 2 minutes or until lightly browned. Drain well on paper towels. Serve immediately.