In a large bowl, combine ground beef, breadcrumbs, egg, Worcestershire sauce, salt, and pepper. Mix gently and form into 4 patties.
Heat olive oil in a large skillet over medium heat. Sear patties for about 4–5 minutes per side until browned. Transfer to a plate.
In the same skillet, add butter, sliced onions, and mushrooms. Cook until softened, about 5–6 minutes.
Sprinkle flour over the vegetables and stir until the flour is absorbed and slightly golden.
Gradually whisk in beef broth, stirring constantly until the gravy thickens, about 3–4 minutes.
Return the patties to the skillet, spoon gravy over them, cover, and simmer on low for another 10–12 minutes until cooked through.
Garnish with chopped parsley if desired and serve hot with mashed potatoes or rice.