Heat oil in a large skillet over medium-high heat. Add onion and sauté for 5 minutes.
Remove onion from skillet and place in a large mixing bowl. Add beef, breadcrumbs, egg, egg white, 1⁄4 cup beef broth, salt and pepper then mix until combined.
Divide meat mixture into 6 equal size patties (approx. 7.2 ounces each). Brown each side of the patties in the skillet for 4-5 minutes on each side; then remove patties from skillet and set aside on a plate.
Add mushrooms to the same skillet and saute for 2-3 minutes. Add beef patties back to the skillet.
In a small bowl, whisk together remaining 1 3/4 cup beef broth, flour, tomato paste, red wine vinegar, Worcestershire sauce, dry mustard and water. Pour over beef and mushrooms, cover and reduce heat to low. Simmer for 20 minutes, stirring occasionally. Garnish with fresh parsley before serving.