Heat a little amount of oil in a small skillet and sweat the onion until soft.
In a large mixing bowl, combine beef, onion, breadcrumbs, egg, ketchup, mustard, and worcestershire sauce. Season with salt and pepper. Mix well and shape them into 4 patties.
Heat 1 tbsp of butter and olive oil in a heavy cast iron skillet over medium heat, add the beef patties and cook for 3-4 minutes on each side. It is okay if the patties are not fully cooked. Transfer the patties to a plate and set aside.
Add the 1 tbsp butter to the skillet and add the onion. Cook until just softened. Add the mushrooms and continue to cook until soft, seasoning with salt and pepper.
Sprinkle flour and toss well until you don't see the white flour. Pour the beef stock and stir to combine everything.
Return the patties to the skillet and simmer for 5 min or until the sauce thickens. Garnish with the parsley if you wish. Serve hot with mashed potatoes.