Combine ground beef, breadcrumbs, egg, onion, garlic, ketchup, Worcestershire sauce, parsley, salt, and pepper.
Shape the mixture into four oval patties.
Heat olive oil in a skillet and sear patties until browned on both sides.
Remove patties from skillet and set aside.
Add mushrooms and onions to the skillet and sauté until golden brown.
Add garlic and cook until fragrant.
Pour in beef broth, Worcestershire sauce, and ketchup; bring to a simmer.
Mix cornstarch with cold water and stir into the gravy to thicken.
Return patties to skillet, spoon gravy over, and simmer for 15-20 minutes.
Garnish with parsley and serve hot.