Add breadcrumbs to a large mixing bowl. Grate onion over the bowl and stir grated onion into the breadcrumbs. There will likely be some onion "juice" that goes into the bowl as well, and that's good. It will add moisture as well as flavor.
Add remaining patty ingredients and use hands to mix until just combined.
Use the side of your hand to lightly score the meat in half. Then score each half into 3 sections. Now you have 6 roughly equally sized sections. Scoop out the meat in each section and form into oval shaped patties.
Heat 1 Tbsp each butter and olive oil in a large skillet over MED HIGH heat. Once hot, add patties and sear about 4-5 minutes per side, until cooked through. Transfer patties to a plate and keep warm.
Reduce skillet heat to MED and add 1 Tbsp butter. Add sliced onions and cook for 3 minutes. Add mushrooms and cook another 4-5 minutes.
Stir in beef broth, scraping the bottom of the skillet to loosen any browned bits. Add tomato paste, soy sauce, Worcestershire sauce, dijon mustard, salt and pepper and whisk or stir to combine well.
In a small bowl combine cornstarch and water and whisk until smooth. Whisk mixture into the beef gravy and simmer until thickened to your liking, about 2-3 minutes.
Add patties back to the skillet and spoon gravy over the top of the patties. Cook another minute or two, until everything is heated through.
Serve patties hot, over mashed potatoes or noodles if you like, with a generous spoonful or two of gravy over the top, sprinkled with minced fresh parsley (if desired).
