Rinse the corned beef under cold water and place it in a large Dutch oven or pot. Sprinkle the seasoning packet over the meat and add enough water to just cover it. Cover the pot, bring to a boil over medium-high heat, then reduce to a simmer. Cook for 2 hours.

Add the potatoes and carrots to the pot, making sure they're covered with the liquid. Add more water if needed. Cover, bring to a boil, then reduce to a simmer. Cook for 15 minutes.

Place the cabbage wedges on top of the pot. They don’t need to be submerged. Cover and cook for another 10 minutes.

Remove the brisket and place it on a cutting board. Slice it into ½-inch slices. Arrange the meat, potatoes, carrots, and cabbage on a platter. Serve warm.