Place corned beef in a large, non-reactive pot. Add the pickling spice and bay leaf, and cover in cold water. Bring to a boil over high heat, cover, and reduce to a simmer for 2.5 hours. Remove cover and add potatoes, carrots, celery, and onions and cook for 15 minutes uncovered. Add cleaned cabbage to the pot and continue to cook for an additional 15 minutes. Remove bay leaf and serve.