Rinse the corned beef under cold water, rubbing the meat gently to remove any thick juices.
Place the corned beef in a large pot (at least 5.5 quarts, preferably 6-7) add the water, bay leaves, black peppercorns, allspice berries, and cloves. Bring to a boil, uncovered, and skim off any scum that rises to the surface (usually white foam). NOTE: you may need to replace some of the peppercorns, allspice berries, or cloves as they are sometimes discarded with the scum).
Boil for about 15-20 minutes until water changes to a caramel color.
Place corned beef in the crock pot, fat-side up, and gently pour the liquid from the pot into the crock pot. Be sure all the contents are transferred to the crock-pot. Cook on high heat for 9 hours.
Using a spatula and tongs, place the corned beef back into the large pot (try to balance the corned beef on the spatula as it will tend to want to come apart at this point) Transfer the remaining contents of the crock-pot back into the large pot, cover, and bring to a gentle boil. Keep pot covered and simmer for 2 1/2 hours.
Remove corned beef using the same method above, place on cutting board and cover tightly in aluminum foil to keep warm.
Using a spoon, remove as many of the peppercorns, allspice berries, and cloves as possible. Add the cabbage and potatoes to the cooking liquid and bring to a boil. Lower heat and simmer until vegetables are tender (20-25 minutes).
Using a slotted spoon, transfer the cabbage to a large platter. Gently trim the fat from the corned beef brisket. Slice the corned beef, across the grain, into thin slices (1/4 - 1/2 inch). Place the slices over the cabbage and add the potatoes to either side. Season the corned beef with pepper. Serve immediately.