Begin by unpacking the corned beef brisket. Rinse it under cold water to remove excess salt and brine. Pat it dry with paper towels.
Place the chopped onions and minced garlic at the bottom of the slow cooker.
Lay the corned beef, fat side up, on top of the onions and garlic.
In a small bowl, combine mustard seeds, black peppercorns, allspice berries, and bay leaf. Sprinkle this spice mixture evenly over the corned beef.
Pour the beef broth around the brisket, ensuring it covers the onions but not the meat.
Cover the slow cooker with the lid, and cook on low heat for about 8 hours or until the meat is tender and easily shredable with a fork.
In the last 2 hours of cooking, add the carrots and baby potatoes on top of the meat.
Once done, remove the corned beef from the slow cooker and let it rest for about 10 minutes before slicing against the grain for serving.
Serve with the cooked vegetables and ladle some of the broth over the top.
Garnish with fresh parsley before serving.