In a large mixing bowl, combine the ground beef, bread crumbs, diced onions, Worcestershire sauce, salt, and pepper. Thoroughly mix the ingredients together with your hands.
Form beef mixture into six oval patties weighing approximately 6 ounces each.
Heat a large skillet over medium-high heat and add the olive oil. Once hot, place the beef patties in the skillet and cook on both sides until the center is no longer pink. You may need to work in batches depending on the size of your skillet.
Transfer the burger patties to a plate and set aside.
Using the same skillet, reduce the heat to medium and make the onion gravy. Add 2 tablespoons of olive oil to the skillet along with the sliced onions. Cook for approximately 10 minutes. Then increase the temperature to medium-high and continue to cook until they are caramelized. Transfer the onions to a bowl or the same plate as the burger patties.
In a medium mixing bowl, whisk together the beef broth, Worcestershire sauce, and ketchup. Add the flour and whisk until no lumps remain.
Pour the broth mixture into the skillet and cook until the sauce begins to thicken.
Add beef patties and onions back to the skillet. Spoon the gravy over the beef, and let the patties cook in the gravy for another 10 minutes.
Sprinkle some chopped parsley over the top for garnish. Serve warm.