In a large mixing bowl, combine the ground beef, diced onion, egg, Panko, Dijon mustard, ketchup, Worcestershire sauce, garlic powder, thyme, salt, and pepper. Take care to mix gently until combined, being cautious not to overwork the meat.
Form the mixture into four uniform oval patties, about 1 inch thick. Using your hands, pack the meat tightly to ensure they hold their shape during cooking.
Heat olive oil in a large skillet over medium-high heat. Once hot, add the patties in batches to avoid overcrowding. Sear for approximately 4 minutes on each side until they develop a nice brown crust and are slightly pink in the center. Transfer the cooked patties to a plate and cover to keep warm.
In the same skillet, add the butter and allow it to melt. Sauté the sliced onions and mushrooms for about 8 minutes, or until they are soft and beginning to brown.
Sprinkle the flour over the cooked onions and mushrooms. Stir well for about a minute to cook the flour slightly before gradually pouring in the beef broth. Stir continuously to avoid lumps and scrape up any bits stuck to the pan.
Stir in the Worcestershire sauce and ketchup. Bring the mixture to a simmer and let it thicken for about 4 minutes. Season with salt and pepper to taste.
Return the beef patties to the skillet, spooning the gravy generously over them. Cover and reduce the heat to low, cooking for an additional 5-7 minutes until the patties reach your desired doneness.
Serve the Salisbury steaks hot, topped with the mushroom-onion gravy and fresh parsley. This dish pairs beautifully with mashed potatoes or buttered noodles.