Begin by preparing your vegetables. Cut the onion, carrots, potatoes, and cabbage, and set them aside.
In your slow cooker, place the quartered onions at the bottom. Add the carrots and potatoes on top.
Rinse the corned beef brisket under cold water to remove excess brine, then place it on top of the vegetables.
In a small bowl, mix the mustard seed, peppercorns, and minced garlic. Rub this mixture over the corned beef.
Pour the beef broth over the brisket and add the bay leaf. Ensure the liquid covers at least two-thirds of the brisket.
Cover the slow cooker with its lid and cook on low for 8 hours.
About an hour before serving, add the cabbage wedges on top of the brisket in the slow cooker to cook until tender.
Once done, use tongs to carefully remove the corned beef from the slow cooker and let it rest for about 10 minutes before slicing against the grain.
Serve the sliced corned beef on a platter with the vegetables and some of the cooking liquid as a sauce.