Place the corned beef (fat cap up) in a large Dutch oven that has enough room so that it fits comfortably (we used a 6 quart enameled Dutch oven).
Add the seasoning pack to the top of the meat. Press the seasoning down gently letting some of it fall around the meat into the pot.
Add enough beef broth and water (in equal parts) to the pot to almost cover the meat. We used 4 cups total liquid for ours. How much liquid to add is going to depend on the size of the pot, size, and shape of the brisket.
Place the pot over medium-high heat and let the liquid come to a boil. Then, lower the heat to medium to medium-low and cover. Keep the liquid at a simmer. If it is boiling too vigorously, lower the heat. If it’s not simmering raise it.
Cook the corned beef for approximately 3½ to 4 hours until it is tender. Check on it occasionally to make sure it is simmering (not boiling) and that there is enough liquid. The liquid will reduce but at least half the roast should be submerged.
To check if it is done insert a large fork into the thickest part of the meat. Then give the fork a twist. You should feel the meat give. You can also pry a piece from one of the corners. If it comes off easily then it is done. The internal temperature will be at least 190°F.
Preheat the oven to 200°F.
Carefully remove the beef from the pot and place it on an oven-safe rimmed baking sheet or dish. Tent it loosely with aluminum foil and place it in the oven to keep warm.
Add about 2 cups of liquid (1 cup broth and 1 cup water) to the remaining broth in the pot. Raise the heat to high and bring it to a boil. Add the vegetables, let the broth come back to a boil.
Then, lower the heat, cover the pot, and cook the vegetables for 15 to 20 minutes or until tender. Keep the liquid at a simmer. Lower or raise the heat as needed. Use a slotted spoon to remove the cabbage, potatoes and carrots from the pot to a plate or platter.
If you would like to brown the top of the corned beef before serving, then uncover it and switch the oven to low broil. Broil if for 3 to 6 minutes until the top reaches the desired color. Remove it promptly.
Slice the corned beef and serve it with the cabbage, potatoes, and carrots. Make sure to add a little broth to the plate for extra flavor.