In a large mixing bowl, combine the ground beef, breadcrumbs, onion, carrot, zucchini, egg, garlic, ketchup, Worcestershire sauce, salt, and pepper. Mix well using your hands or a spoon.
Shape the mixture into 12 equal-sized patties about 2/3 inch thick.
Heat the vegetable oil in a large skillet over medium heat. Add some patties and cook them for 4 to 5 minutes on each side, or until browned and cooked through. Work in batches as needed.
If using, sprinkle the rissoles with fresh parsley. Serve the rissoles hot with your favorite sides.