In a large mixing bowl, combine the ground beef, Panko bread crumbs, diced onion, Worcestershire sauce, salt, and black pepper. Mix thoroughly using clean hands until all ingredients are evenly incorporated, taking care not to overwork the meat.

Divide the mixture into six equal portions and shape each into an oval patty, approximately 6 ounces in weight. Ensure the patties are uniform in thickness to promote even cooking.

Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Once the oil is hot, place the patties in the skillet, working in batches if necessary to avoid overcrowding. Cook on both sides until browned and the internal temperature reaches 160°F, or until the center is no longer pink. Transfer the cooked patties to a plate and set aside.

Using the same skillet, reduce the heat to medium and add 2 tablespoons of olive oil. Add the sliced onions and cook for approximately 10 minutes, stirring occasionally, until softened. Increase the heat slightly and continue cooking until the onions are caramelized and golden brown. Remove the onions from the skillet and set aside.

In a medium bowl, whisk together the beef broth, Worcestershire sauce, ketchup, and flour until smooth and free of lumps. Pour the mixture into the skillet and cook over medium heat, stirring continuously, until the gravy thickens to the desired consistency.

Return the cooked patties and caramelized onions to the skillet. Spoon the gravy over the patties and allow them to simmer gently for approximately 10 minutes, ensuring the flavors meld together. Garnish with freshly chopped parsley before serving. Serve warm.