In a large bowl, combine ground beef, egg, bread crumbs, pepper, salt, onion powder, garlic, and Worcestershire sauce. Form into thick patties.
Heat oil in a large skillet over medium heat. Fry the patties and onion in the oil until patties are well browned.
Remove the meat patties and keep warm on a plate.
Sprinkle flour over the onions and drippings in the skillet. Stir in flour with a fork, scraping up meat bits from the bottom.
Gradually mix in the beef broth. Season with salt. Simmer and stir over medium-low heat for about 5 minutes until the gravy thickens.
Reduce heat to low, return patties to the gravy, cover, and simmer for an additional 15 minutes.