Heat butter over medium heat in a big heavy skillet; cook and stir onion, green onions, celery, carrot, and garlic for about 5 minutes or until it is fragrant. Cover the skillet with a cover and cook for about 5 more minutes, stirring occasionally until the carrot is soft.
In a vegetable mixture, add 1/3 cup ketchup, Worcestershire sauce, salt and pepper; cook for about 1 minute until warm.
In a big bowl, combine ground beef, sausage, vegetable mixture, bread crumbs, parsley and eggs; form into a loaf and place in a 2-inch high sided rectangular baking pan. Cover the loaf with 1/3 cup ketchup remaining.
Bake in the preheated oven, about 1 hour until the center is no longer pink. A thermometer inserted in the middle for instant reading should read at least 160°F (70°C)