In a large bowl, combine all patty ingredients and mix until just combined. Form into 8 thin patties.
Heat vegetable oil in a skillet over medium-high heat. Fry patties until browned on both sides (work in batches if needed). Remove and set aside.
Reserve about 2 tbsp of oil in the pan. Add sliced onions and cook until soft and caramelized, about 10–12 minutes.
Add garlic and cook for 1 more minute.
Sprinkle flour over onions, stir constantly for 1 minute until lightly browned.
Slowly whisk in 2 cups of beef broth, Worcestershire, ketchup, and browning sauce. Stir and simmer until slightly thickened.
Return patties to skillet, spoon gravy over top, cover, and simmer on low for 20 minutes. Add more broth if needed to keep gravy loose.
Serve hot with mashed potatoes, rice, or vegetables.