Rinse the corned beef under cold water to remove excess salt and place it in a large pot or slow cooker.
Add onion, garlic, bay leaves, black peppercorns, mustard seeds, and the included spice packet if available.
Pour in enough water or beef broth to fully cover the brisket.
For stovetop cooking, bring to a boil, then reduce heat to low, cover, and simmer for 3 to 4 hours until tender.
For slow cooker cooking, cook on low for 6 to 8 hours or on high for 4 to 5 hours.
Add carrots and potatoes during the last 1 to 1.5 hours of cooking to avoid overcooking.
Remove the brisket and let it rest for 10 minutes before slicing against the grain.
Serve slices with vegetables and some cooking broth.