Coarsely chop enough onions and carrots to make 1 cup each.
In large pot place onions, carrots, corned beef, malt vinegar, Irish stout, mustard seed, coriander seeds, peppercorns, dill seed, allspice and bay leaves. Add water to barely cover the meat. Cover pot and bring to a boil over high heat. Reduce heat and simmer until meat is tender when pierced with a fork, about 2 1/2 to 3 hours.
Meanwhile, cut remaining onions into wedges. Cut remaining carrots into 2-inch lengths. Cut cabbage in half through core then into wedges. Scrub potatoes.
Add onions, carrots and potatoes to corned beef and place cabbage on top. Cover and return to a boil over high heat; reduce heat and simmer until cabbage is tender when pierced, 15 to 20 minutes.
Using tongs and a slotted spoon, remove beef to a cutting board; cut off and discard fat, slice meat across the grain and place on warm platter. With a slotted spoon scoop out vegetables and arrange around the meat.