Place corned beef in a large pot or Dutch oven and cover with water. Add the spice packet that came with the corned beef. Cover the pot, bring to a boil, reduce to a simmer, and cook for about 2 1/2 hours.
Add whole potatoes and carrots, and cook until the vegetables are almost tender. Add cabbage and cook for another 20 minutes.
Remove the meat and let it rest for 15 minutes. Slice across the grain.
Notes
This dish pairs well with a side of mustard or horseradish sauce.