In a medium bowl gently mix the ground beef, breadcrumbs, egg, salt, pepper, and soy sauce until just combined, do not overmix.
Divide the beef mixture into 4 even mounds. Form into ½-inch thick oval patties, about 5-inches long and 2 ½-inches wide. Cover and chill the patties in the refrigerator for 15 minutes.
Cut the onion into ¼-inch thick slices. Cut the mushrooms into ¼-inch thick slices. Mince the garlic. Set aside to use for the sauce.
Heat olive oil in a 12-inch cast iron skillet or nonstick pan over medium-high heat. Once the oil is hot, add the beef patties.
Cook until golden brown, 3 to 4 minutes. Flip and reduce the heat down to medium. Cook until the internal temperature reaches 140 to 145ºF (60 to 63ºC) for medium-well, or 150 to 155ºF (65 to 68ºC) for well-done, about 3 to 5 minutes. There will be some carryover cooking of the meat after resting. Transfer to a clean plate.
Carefully wipe the pan clean or keep the drippings for a more flavorful sauce. Heat the butter in the skillet over medium heat. Once melted add the onions. Saute until softened, about 3 minutes. Add the mushrooms, salt, and pepper. Saute until the mushrooms are tender, 3 minutes. Add the garlic and saute for 30 seconds.
Add the tomato paste and flour, stir and cook for 30 seconds. Add the balsamic vinegar, stir and cook for 15 seconds. Slowly pour in the beef stock, stir and cook until thickened, about 2 minutes.
Place the steaks back in the pan, turning to coat in the sauce to warm.
Garnish with parsley.
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