Begin by assembling all of the ingredients. Place the corned beef in a Dutch oven and pour in enough water to fully submerge it. Add the contents of the spice packet, cover the pot, and bring it to a boil. Once boiling, reduce the heat and allow the beef to simmer gently for approximately two hours, or until it reaches a near fork-tender state.

While the corned beef is cooking, prepare the vegetables. Cut the red potatoes in half, peel the carrots, and slice them into 3-inch segments. Chop the cabbage into small wedges.

After the beef has been cooking for two hours, add the potatoes and carrots to the pot. Continue cooking until the vegetables are nearly tender, and the corned beef is completely fork-tender, which should take about 10 minutes. Finally, introduce the cabbage wedges and cook for an additional 15 minutes, or until the cabbage softens.

Once the meat is done, remove it from the pot and let it rest for 15 minutes. Keep the broth and vegetables warm in the Dutch oven. Slice the meat across the grain before serving it alongside the cooked vegetables and the flavorful broth.