Prepare the Hamburger Steaks:
In a large mixing bowl, gently combine the ground beef, breadcrumbs, egg, Worcestershire sauce, garlic powder, onion powder, salt, and pepper. Mix just until combined, then form into 4 oval-shaped patties.

Cook the Patties:
Heat vegetable oil in a large skillet over medium-high heat. Place the patties in the skillet and cook for about 4–5 minutes on each side, or until nicely browned. Transfer them to a plate and set aside.

Make the Onion Gravy:
In the same skillet, add the sliced onions. Cook over medium heat for 8–10 minutes, stirring occasionally, until they’re soft and golden brown.
Sprinkle flour over the onions and stir well, cooking for another 1–2 minutes to make a roux.
Slowly pour in the beef broth (and chicken broth if using), stirring continuously to prevent lumps. Add Worcestershire sauce and season with salt and pepper. Let it simmer for 5–7 minutes, or until thickened.

Finish Cooking:
Return the hamburger steaks to the skillet, nestling them into the gravy. Spoon some of the sauce over each patty. Cover the skillet and let it simmer for 10–15 minutes, or until the patties are fully cooked through.

Serve:
Serve warm with mashed potatoes, rice, or buttered noodles. Optional: garnish with chopped fresh parsley.