Rinse the corned beef brisket thoroughly under cold water to remove any excess brine. Trim any large pieces of hard fat from the brisket if desired, leaving a thin layer for flavor.

Place the rinsed corned beef brisket in a large Dutch oven or heavy-bottomed pot. Add the spice packet (from the corned beef packaging), quartered yellow onion, smashed garlic cloves, bay leaves, and black peppercorns to the pot.

Pour enough cold water over the brisket to fully submerge it by at least an inch. Bring the water to a rolling boil over high heat. Once boiling, reduce the heat to low, cover the pot tightly, and simmer gently for 3 to 3.5 hours, or until the corned beef is fork-tender. Cooking time will vary based on the size and cut of your brisket.

Once tender, carefully remove the corned beef from the pot and transfer it to a cutting board. Tent loosely with aluminum foil to keep warm and allow it to rest for at least 15-20 minutes. This resting period is crucial for juicy, tender meat.

While the beef is resting, skim off any excessive fat from the cooking liquid in the Dutch oven using a large spoon or ladle. Discard the skimmed fat.

Add the halved or quartered red potatoes and 2-inch carrot chunks to the simmering broth. Bring the liquid back to a gentle boil and cook for about 15 minutes, or until the potatoes and carrots are almost tender.

Add the cabbage wedges to the pot, nestling them among the other vegetables. Continue to cook for another 10-15 minutes, or until the cabbage is tender-crisp and the potatoes and carrots are fully cooked through.

Slice the rested corned beef against the grain into thick pieces. Arrange the sliced corned beef on a large platter or individual plates alongside the cooked potatoes, carrots, and cabbage.

Drizzle a little of the flavorful cooking broth over the meat and vegetables. Garnish with fresh chopped parsley, if desired. Serve immediately with whole grain mustard or horseradish sauce on the side.