In a large mixing bowl, combine the lean ground beef, Italian bread crumbs, minced rosemary, and 1 teaspoon of Worcestershire sauce. Season with salt and pepper. Mix gently until all ingredients are well incorporated, but avoid overmixing to keep the patties tender.
Divide the beef mixture into four equal portions and shape each into a patty, about ¾ inch thick. Press a slight indentation in the center of each patty to help them cook evenly.
Heat the olive oil and butter in a large skillet over medium heat. Once hot, add the patties to the skillet and cook for about 4-5 minutes on each side, or until they are browned and cooked through. Remove the patties from the skillet and set aside.
In the same skillet, add the sliced onions and sauté for about 5 minutes, or until they are soft and translucent. Stir occasionally to prevent burning.
Add the remaining teaspoon of Worcestershire sauce, beef broth, and ketchup to the skillet with the onions. Bring the mixture to a gentle simmer. In a small bowl, mix the cornstarch with a couple of tablespoons of water to create a slurry. Gradually add this to the skillet while stirring to thicken the gravy.
Return the cooked hamburger steaks to the skillet, spooning the gravy over the top. Let everything simmer together for an additional 2-3 minutes. Serve hot with your favorite sides, such as rice or mashed potatoes, and enjoy the delicious flavors!
