In a large bowl, combine the ground beef, egg, breadcrumbs, Worcestershire sauce, salt, and pepper. Mix until well combined and shape into 2 patties.
Heat olive oil in a large skillet over medium heat. Add the patties and cook for 4-5 minutes on each side until browned. Remove and set aside.
In the same skillet, add mushrooms and onions. Cook for about 5 minutes or until softened.
Return the patties to the skillet. Add the beef broth. Bring to a simmer, reduce heat to low, and cook for 10 minutes.
Stir in the cornstarch mixture and cook for another 2-3 minutes until the gravy thickens. Adjust seasoning with salt and pepper. Serve hot.