Though it's fashionable to announce that corned beef and cabbage is more Irish-American than true Irish, the fact is that — while "bacon" (i.e., cured pork loin) and cabbage is more common in Ireland today — corned beef has long been happily consumed by the Irish, especially on special occasions, like St. Patrick's Day, for centuries, with cabbage, potatoes, and other accompaniments.
Place corned beef in a large, 6-8 quart pot. Cover the beef with an inch of water. Add spices. Bring to a boil over high heat, and then reduce heat to a simmer. Simmer for 2-3 hours, until the corned beef is fork tender.
Remove the meat from the pot and transfer to a cutting board. Reserve cooking liquid for boiling cabbage.
Once you have removed the corned beef, add the cabbage and optional vegetables to the pot. Taste the cooking liquid; if it is too salty, add more water to the pot. Raise the heat until the liquid is simmering well, about medium-low. Simmer until the cabbage and any other vegetables are cooked through, about 15-30 minutes.
Cut the meat against the grain into ½-inch thick slices. Serve along with the cabbage, vegetables, and a little cooking liquid in a bowl