Make the patties: In a large bowl, combine the ground beef, breadcrumbs, egg, Worcestershire sauce, ketchup, garlic powder, onion powder, salt, and pepper. Mix gently until combined. Divide the mixture into 4 equal portions and form into patties.
Cook the patties: Heat olive oil in a large skillet over medium-high heat. Cook the patties for about 4-5 minutes per side, or until browned and cooked through. Remove from the skillet and set aside.
Prepare the gravy: In the same skillet, melt butter over medium heat. Add the sliced onions and sauté until soft and golden. Sprinkle the flour over the onions and stir, cooking for 1 minute.
Add the broth: Slowly add the beef broth while whisking constantly to avoid lumps. Stir in the Worcestershire sauce and ketchup. Simmer for 5-7 minutes, or until thickened. Season with salt and pepper.
Simmer the patties: Return the cooked patties to the skillet and let them simmer in the gravy for about 5 minutes.
Serve: Serve the hamburger steak patties hot, topped with the onion gravy. Enjoy with mashed potatoes, rice, or your favorite vegetables.
