Separate 12 large outer leaves from the cabbage head; set aside the remaining cabbage head. Remove the center vein from each leaf so it becomes more pliable. Soften the cabbage leaves in boiling water for 2 to 3 minutes. Remove from water with a slotted spoon; set aside until cool enough to handle.

Chop 1 cup of cabbage from the remaining cabbage head. Save any leftover cabbage to use in a salad, soup or stir-fry dish. Cook and stir the chopped cabbage, onion and celery in oil over medium heat in a medium, non-stick skillet until onion is translucent, about 10 minutes. Add corned beef hash, breaking it up with a spoon; mix gently. Heat over medium heat for about 5 minutes. Add 1/4 cup spaghetti sauce and breadcrumbs, mix well. Cool slightly.

Spoon about 1/4 cup of the corned-beef mixture onto each cabbage leaf. Roll, tucking the ends in. Arrange cabbage rolls, seam side down, in a shallow baking dish. Pour remaining spaghetti sauce over cabbage rolls. Bake at 350ºF covered for about 25 minutes, until heated through. To serve, spoon spaghetti sauce over cabbage rolls; sprinkle with parsley.