In a large bowl, combine ground beef, onion, garlic, breadcrumbs, egg, Worcestershire sauce, salt, and pepper. Mix gently until just combined.
Divide mixture into 4 equal portions. Shape into 3/4-inch thick patties. Add more breadcrumbs if the mixture is too wet.
Heat olive oil in a large skillet. Cook patties over medium-high heat for 4–5 minutes per side, until browned. Transfer to a plate.
In the same skillet, melt butter (or olive oil) over medium heat. Add mushrooms and sauté for 3–4 minutes until browned.
Sprinkle flour over the mushrooms, whisk to combine, and cook for 1 minute.
Gradually add beef broth and vegetable broth, stirring continuously. Bring to a simmer.
Add soy sauce (if using), salt, and pepper. Cook until slightly thickened (approx. 5 minutes).
Return patties to the skillet or serve gravy over them. Garnish and serve with mashed potatoes or rice.