Rinse the corned beef and place it in a crock pot with 3 1/2 cups of cold water. Set the crock pot on high, cover, and once steaming rapidly, reduce the heat to medium and continue cooking until the meat is tender, about 2 1/2 hours.
Remove the meat from the crock pot, place the vegetables in the pot and then cover with the meat. Raise the heat to high. When the mixture is steaming, reduce the heat to medium and cook until the vegetables are tender, about 45 minutes.