01 - Rinse the corned beef brisket thoroughly under cold running water to remove excess brine. Transfer to a large stockpot and add the spice packet, bay leaves, peppercorns, mustard seeds if using, quartered onion, and smashed garlic.
02 - Pour in enough water to cover the beef by at least 1 inch. Bring to a rolling boil over high heat, then reduce to low, cover tightly, and maintain a gentle simmer for 2½ hours. Skim any foam that rises to the surface periodically.
03 - After 2½ hours of simmering, carefully add the halved potatoes and carrot pieces to the pot. Continue simmering covered for 20 minutes, or until potatoes begin to soften.
04 - Arrange the cabbage wedges on top of the simmering vegetables. Cover and cook for an additional 20–25 minutes until the cabbage is tender and all vegetables are cooked through.
05 - Remove the corned beef from the pot and transfer to a cutting board. Let rest for 10 minutes before slicing against the grain into thin slices.
06 - Arrange sliced beef and vegetables on a large serving platter. Ladle some of the cooking broth over the top for added moisture if desired. Serve immediately while hot.