In a large bowl, mix together the ground beef, egg, pepper, salt, onion powder, garlic powder, and Worcestershire sauce. Form into 4 balls, and flatten into patties.
Heat the butter in a large skillet over HIGH heat. Brown the patties and remove from heat (will still be uncooked in the middle) Saute onion in the remaining butter soft.
Sprinkle flour over the onions and drippings in the skillet. Pour in Sherry and stir in flour with a fork, scraping bits of beef off of the bottom as you stir. Gradually mix in the beef broth. Season with garlic or salt if desired. Simmer and stir over medium-low heat for about 5 minutes, until the gravy thickens.
Return patties and cover with gravy. Turn heat to low, return patties to the gravy, cover, and simmer for another 15 minutes.