In a large Dutch oven or large soup pot, add the sliced onion along with the pickling spices, and the Corned Beef. Add enough water to cover the Corned Beef by an inch, about 6 cups.
Bring the onion, water and beef to a simmer, then cover and keep the heat on low. Keep simmering the meat in the liquid, covered, until fork tender, about 3-4 hours. The internal temperature of the meat should reach 160 degrees F.
Remove the meat from the pot and place on a large plate or platter; cover with foil. Transfer the meat to a pre-heated 200-degree oven to stay warm.
Add the vegetables to the pot. If there isn’t enough liquid because some of it has evaporated during the cooking process, add another 1-2 cups of water, or enough to come up to the top of the vegetables. Raise the heat to medium and cook the vegetables, covered, until fork tender. About 25-30 minutes.
The last 5-10 minutes of cooking the vegetables, add the meat and any accumulated juices back to the pot. Stir to combine.