Rinse the corned beef under cold water to remove excess salt.
Place corned beef in a large pot and cover with water or broth.
Add garlic, pepper, mustard seeds, and spice packet if included.
Bring to a boil, then reduce heat and simmer for 2.5–3 hours.
Add potatoes, carrots, and onion to the pot.
Continue cooking for 20–25 minutes until vegetables are tender.
Add cabbage wedges and cook for another 10–15 minutes.
Check that the meat is fork-tender.
Remove corned beef and slice against the grain.
Serve with vegetables and broth.