In a mixing bowl, combine hamburger meat, italian bread crumbs, rosemary and 1 tsp Worcestershire sauce. Divide the meat into four and shape the patties into an oval shape.
In a large skillet heat 2 T olive oil and 1 tsp butter over medium high heat. Add the patties to the skillet and fry them on each side until cooked through.
Remove the patties from the skillet and set aside until ready to use. Add onions to the skillet and cook them over medium heat until they are caramelized. (clear and tender).
Once onions are cooked, add beef broth, ketchup, 1 tsp Worcestershire sauce, and salt and pepper to taste. In a small bowl, whisk together cornstarch and 1 T beef broth to make a thin paste and then whisk this into the beef broth gravy mixture. Bring the mixture to a boil and reduce heat to low. Add the patties back to the skillet with the gravy and heat through.
Serve with mashed potatoes, or over a bed of rice.