Place the corned beef brisket in a dutch oven pot and add the spice packet. Add enough water to cover the brisket by 2 inches.
Add the carrots, bay leaves, onions, and celery. Turn the heat to high and bring it to a boil. Turn the heat then down to a simmer. Let it cook until it's fork tender. The brisket should slide off the fork easily when it's down. This will take approximately 2 1/2 hours.
In the last 15-20 minutes of cooking, add the potatoes and cabbage. Cover and let it simmer until tender. If you find that the vegetables are cooked before the brisket, simply remove the vegetables and continue cooking the meat.
To serve, slice the corned beef and serve with cabbage and potatoes. It's optional to serve it with the liquid.