In a large bowl, combine beef with the egg, breadcrumbs, onion, Italian seasoning, salt and pepper. Do NOT overwork the meat. Divide into 4-5 oval patties that are about ½ inch thick.
In a skillet, heat olive oil over medium high heat, cook for 5 minutes per side or until browned (internal temperature must reach 160°F/71°C). Remove onto a plate, cover with foil and set aside.
In the same skillet, melt the butter, and sauté the mushrooms and onions for 4-5 minutes or until the onion is translucent.
Add the garlic, and cook for 30 seconds.
Add the flour, and cook for 30 more seconds while stirring. Add the beef broth gradually while whisking. Bring the mixture to a boil, and simmer for 3 minutes or until the sauce thickens and looks like a glaze.
Season with Worcestershire sauce, salt and pepper.
Return the hamburger steaks to the skillet, spoon the sauce over the steaks, and cook for 5 more minutes.
Remove from heat, garnish with parsley and serve over mashed potatoes with steamed broccoli or green beans.