Rinse the corned beef brisket under cold water to remove excess salt. Place it in a large pot or Dutch oven.
Add the quartered onion, minced garlic, black peppercorns, and bay leaves to the pot. Pour in the beef broth, ensuring the brisket is covered.
Bring the mixture to a boil over medium-high heat. Once boiling, reduce the heat to low, cover, and simmer for about 2.5 to 3 hours, or until the meat is tender.
After the brisket has cooked, remove it from the pot and set it aside to rest for 10-15 minutes.
While the meat is resting, add the cabbage wedges, carrots, and potatoes to the pot. Cook for about 20-25 minutes, or until the vegetables are tender.
Slice the corned beef against the grain into thin slices. Serve with the cooked vegetables and a dollop of Dijon mustard if desired.