In a large Dutch oven or large soup pot, add the sliced onion 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.