Whisk the egg in a medium bowl. Add the breadcrumbs, 1 T. Worcestershire, and salt, stir to combine. Add the beef and mix until combined. Divide the mixture into 4 portions and shape each into an oval patty about ½-inch thick.
Preheat 1 T. oil in a large skillet over medium heat until shimmering. Add the patties and sear until a dark brown crust forms, about 5 minutes. Flip the patties and cook until the second side is browned, 4 to 5 minutes more. Transfer the patties to a clean platter.
In the same pan add 1 T. butter, scraping up the browned bits from the bottom. Add the mushrooms and onions. Cook, stirring frequently, until the mushrooms are tender and the onions are beginning to brown, about 8 minutes. Add the garlic and tomato paste and cook until fragrant, about 1 minute. Mix the beef broth, remaining 1 T. Worcestershire with 1 T. cornstarch and add to the pan, stirring until combined.
Return the patties and any accumulated juices to the pan, cover, and simmer until the patties are cooked through and the sauce has thickened slightly, 10 to 12 minutes.
Serve and enjoy!