Combine the ground beef, breadcrumbs, egg, onion, mustard, Worcestershire sauce, salt, and pepper in a large bowl. Use your hands to mix until the mixture becomes sticky and cohesive, about 2 to 3 minutes.

Divide the mixture into five equal portions, shaping each into a patty weighing approximately 6 ounces.

Heat the olive oil in a large skillet over medium-high heat. Once hot, add the patties and cook for 4 to 5 minutes per side, or until fully cooked. Transfer the patties to a plate and set aside.

If more than a teaspoon of grease remains in the skillet, carefully discard the excess to avoid an overly greasy gravy. Return the skillet to medium-high heat and melt the butter. Add the mushrooms, onion, and garlic, and sauté for 3 to 5 minutes, or until the onions are soft and translucent.

Sprinkle the flour over the vegetables and cook for 2 minutes, stirring constantly. Slowly pour in the beef broth while continuing to stir. Add the ketchup and Worcestershire sauce and simmer until the gravy thickens, stirring occasionally.

Return the patties to the skillet, spoon the gravy over them, and let them warm through for 2 to 3 minutes. Garnish with chopped parsley, if using, and serve hot.