Mix onion, breadcrumbs, ground beef, garlic, egg, ketchup, bouillon cube, Worcestershire sauce, and Dijon mustard. Shape into 5 oval patties.
Brown patties in a large skillet over medium-high to high heat, then remove and set aside.
Cook garlic, onion, and mushrooms in the skillet. Add butter and flour, then gradually add beef broth and water. Stir in Dijon mustard and Worcestershire sauce until the gravy thickens.
Return patties to the gravy and simmer until cooked through. Ensure the patties reach 160°F / 71°C internally before serving.