Place the corned beef, onion, carrots, and celery in a large pot or dutch oven. Sprinkle in the salt and spice packet. Fill the dutch oven with water until all the ingredients are covered, approx 3 quarts.
Turn on the heat under the dutch oven on high, and bring the water to a simmer. Skim the fat off the water, cover, turn down the heat to low, and cook for 3 hours.
Now add your halved potatoes, making sure they are submerged in the hot water, cover and cook for a ½ hour.
Last, add your cabbage, cover, and cook for another ½ hour, or until the potatoes are fully cooked.
Once the potatoes are fully cooked, remove the corned beef from the dutch oven and let rest on a cutting board for 25 minutes. Slice up the corned beef, against the grain, into whatever sized portion you like.
Serve up the corned beef with some potato, celery, carrot, and cabbage. Make sure to drizzle some cooking liquid over everything too!
Enjoy!