In a large cast-iron pot or Dutch oven over medium heat, heat oil; once the oil is hot, add ground beef, and cook until water evaporates, about 5 minutes. Add onions, bell pepper, and celery cook for 3 minutes, then add garlic, bay leaves, Worcestershire, oregano, savory, salt, cayenne, and gizzards; cook for 1 minute. Stir in 1.5 cups of gizzard stock, rice, and half the green onions, making sure it’s coated evenly.