In a mixing bowl, combine the ground beef, Italian bread crumbs, rosemary, and 1 teaspoon Worcestershire sauce. Divide the meat into four and shape the patties into an oval shape.
In a large skillet heat 2 tablespoons of olive oil and 1 teaspoon of butter over medium-high heat.
Add the patties to the skillet and fry them for 4-5 minutes on each side until they are cooked through. Remove the patties from the skillet and set.
Add the onions to the same skillet and cook them over medium heat until they are tender and browned.
Once the onions are cooked, add the beef broth, ketchup, 1 teaspoon Worcestershire sauce, and salt and pepper to taste.
In a small bowl, whisk together cornstarch and 1 tablespoon of the liquid to make a thin paste, 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.