01 - Rinse the corned beef brisket under cold running water to remove excess brine. Place the meat in a large stockpot.
02 - Pour in the water, beef broth, spice packet, bay leaves, peppercorns, allspice berries (if using), onions, and garlic. Bring the mixture to a rolling boil over high heat.
03 - Reduce heat to low, cover the pot, and simmer gently for 2 hours. Skim any foam that rises to the surface occasionally.
04 - Add the halved potatoes and carrot pieces to the pot. Cover and continue simmering for 30 minutes until potatoes begin to soften.
05 - Gently place cabbage wedges into the simmering liquid. Cover and cook for an additional 15-20 minutes until all vegetables are fork-tender.
06 - Carefully remove the brisket from the pot and transfer to a cutting board. Let rest for 10 minutes before slicing against the grain into thin strips.
07 - Arrange sliced brisket and vegetables on a large serving platter. Ladle warm cooking broth over the top for added moisture and flavor. Serve immediately while hot.