Cover with 12 cups cold water, or more to cover the meat.
Bring back to a simmer, partially cover the pan, simmer for 3 – 4 hours (adding more water as necessary to keep beef covered), until beef is tender, but not falling apart.
Remove the beef from the pot, wrap in foil, and keep warm.
Strain the cooking liquid, and add it back to the pot, discarding the onion and spices.
Bring the liquid back to a simmer, and add the vegetables in this order — (you should end up with all the veggies in the pot together) cabbage—give it about 4 minutes, then add turnips — give them about 5 minutes, then add carrots — give them about 3 minutes, and then add potatoes, simmering for about 10 – 15 more minutes.
They should all be fork tender.
David serves it this way — slice corned beef thinly against the grain, place in a shallow soup bowl with vegetables, and ladle about ½ cup stock over all, with mustard and/or horseradish on the side.
We have it in dinner plates sliced, with our veggies on the side, and plenty of butter and salt and pepper on them.
Also great with crusty bread, and maybe some mustard or horseradish on the side.