Mix bread cubes with milk or water until bread is softened. Mix together ground beef, softened bread cubes and rest of ingredients. (Not the gravy ingredients though). Mix well; form into patties. Pan fry or broil to desired doneness.
Place cooked hamburgers on a warm platter and keep warm while preparing the gravy. Remove oil, leaving brown particles in pan. Pour broth into pan and heat to boiling, stirring and loosening brown particles,. Mix flour with water to make a smooth paste. Slowly add to heated broth, stirring constantly, until smooth. Add salt and pepper.
Serve the hamburger steak on hot steamed rice, with fried egg on the hamburger and gravy over all.