Mix ground beef, breadcrumbs, grated onion, garlic powder, onion powder, salt, pepper, and egg just until combined.
Divide into 6 and form thin patties. Press the center slightly thinner.
Heat oil in a pan over medium-high heat. Cook patties 2–3 minutes per side until browned. Set aside.
Mix beef base, warm water, soy sauce, and Worcestershire sauce.
In the same pan, cook mushrooms in one layer until browned. Add butter, onion, and garlic; cook until softened.
Sprinkle in flour and cook for a minute.
Pour in the broth mixture while stirring. Simmer until thickened. Season to taste.
Return patties and spoon the gravy over. Simmer until heated through. Serve with rice.