1 pound carrots, scraped and cut into 2-inch lengths
1-1/2 pounds small thin-skinned potatoes, scrubbed
3 pounds cabbage, cut in wedge
In a large stockpot (8- to 10-quart) place chopped onions and carrots, corned beef and any liquid, vinegar, mustard seed, coriander, peppercorns, dill, allspice, and bay leaf. Add water just to cover beef. Cover pot and bring to a boil over high heat. Simmer until meat is tender when pierced, about 2 to 3 hours. Add onion wedges, carrot pieces, and potatoes to pot with corned beef. Place cabbage wedges on top. Cover and return to boil over high heat (8 to 20 minutes). Reduce heat and simmer until cabbage is tender, about 15 to 20 minutes. Using a slotted spoon, remove vegetables to warm serving dishes. Using tongs and slotted spoon, remove beef to cutting board; remove and discard fat, and slice beef across the grain. Serve with coarse-grained Dijon mustard.