Place corned beef, pepper, allspice, bay leaves, and salt into a large pot along with 3 quarts of water. Cover and set over high heat until boiling. Reduce heat to low and cook at a gentle simmer for 2 1/2 hours. Add the carrots, onions, potatoes, and celery. Return to a simmer and cook uncovered for 15 minutes. Add the cabbage and cook an additional 15-20 minutes until the potatoes and cabbage are tender. Remove bay leaves and serve.