In a large mixing bowl, gently combine the ground beef with the egg, breadcrumbs, diced onion, Italian seasoning, salt, and pepper. Avoid overmixing to maintain the texture of the meat. Shape the mixture into 4-5 oval patties, roughly ½ inch thick.

Heat the olive oil in a skillet over medium-high heat. Cook the patties for about 5 minutes per side until browned and cooked through. The internal temperature should reach 160°F/71°C. Transfer the patties to a plate, cover with foil, and set them aside.

Using the same skillet, melt the butter. Sauté the sliced mushrooms and onions for about 4-5 minutes, or until the onions are soft and translucent.

Stir in the minced garlic and cook for an additional 30 seconds.

Sprinkle the flour over the mixture and stir continuously for another 30 seconds. Gradually pour in the beef broth while whisking to prevent lumps. Bring the gravy to a boil, then reduce the heat and let it simmer for 3 minutes, or until the sauce has thickened to a glossy consistency.

Stir in the Worcestershire sauce, salt, and pepper to season the gravy.

Return the cooked hamburger steaks to the skillet, spooning the gravy generously over the top. Let them cook in the sauce for another 5 minutes.

Remove from heat, sprinkle with freshly chopped parsley, and serve alongside mashed potatoes with steamed broccoli or green beans for a hearty meal.