Prepare the Meat Mixture: In a large mixing bowl, gently combine the ground beef, Panko breadcrumbs, beaten egg, 1 tablespoon of Worcestershire sauce, and half of the French onion soup mix. Use a fork to mix just until combined to keep the meat tender.
Form the Patties: Divide the mixture into 4 equal portions. Shape them into oval patties, about ¾-inch thick. Press a shallow indent into the center of each patty.
Sear the Steaks: Heat the olive oil in a large skillet over medium-high heat. Add the patties and sear for 3-4 minutes per side until a brown crust forms. Remove the patties to a plate (they will not be fully cooked through yet).
Sauté the Onions: Reduce the heat to medium. Melt the butter in the same skillet. Add the sliced yellow onions and cook for 5-7 minutes, scraping up any browned bits from the bottom of the pan, until the onions are softened and beautifully caramelized.
Create the Gravy: Sprinkle the flour over the onions and stir constantly for 1 minute. Slowly whisk in the beef broth, the remaining half packet of French onion soup mix, and 1 tablespoon of Worcestershire sauce. Bring the mixture to a gentle simmer.
Simmer and Thicken: Return the seared steaks (and any juices from the plate) to the skillet. Reduce the heat to medium-low, cover partially, and let simmer for 10-15 minutes, or until the steaks are cooked through and the gravy has thickened.
Serve: Garnish with freshly chopped parsley and serve hot over mashed potatoes or egg noodles.