Place the brisket in a large Dutch oven and add enough water to just cover it. Add the spice packet and bring the water to a boil. Cover the pot, reduce the heat to low and simmer for 30 minutes, then skim any gray foam from the top of the pot and discard it. Cover and resume simmering until the corned beef is just about fork-tender, another 90 minutes.

While the corned beef is simmering, prepare the vegetables. Cut the baby potatoes in half (chunks if using larger potatoes). Peel and quarter the onion. Peel the carrots and cut into 1 ½- to 2-inch pieces. Cut the cabbage in half, remove the core, and cut it into large slices or wedges.

When the corned beef has cooked for 2 hours, add the potatoes, onion, and carrots. Simmer until the vegetables are almost tender and meat is fork-tender, 15-20 minutes. Add the cabbage, removing some of the broth if needed so it fits, and cook until tender, about 15 more minutes.

Turn off the heat. Remove the corned beef and let it rest for 15 minutes, allowing the broth and vegetables to remain in the Dutch oven. Slice the meat across the grain and serve with the vegetables and broth.