Place corned beef in a large Dutch oven; cover with water. Add the onion, carrot, celery and pickling spices. Bring to a boil. Reduce heat; cover and simmer for 2-1/2 to 3 hours or until meat is tender.
Transfer corned beef to a 13-in. x 9-in. baking dish; discard broth and vegetables. Score the surface of meat with shallow diagonal cuts.
In a small bowl, combine brown sugar and mustard; spread over meat. Drizzle with pickle juice. Bake, uncovered, at 325° for 1 hour, basting occasionally.