Place corned beef in large pot or Dutch oven and cover with water. Add the spice packet that came with the corned beef. Cover pot and bring to a boil, then reduce to a simmer. Simmer approximately 50 minutes per pound or until tender.
Add whole potatoes and carrots, and cook until the vegetables are almost tender. Add cabbage and cook for 15 more minutes. Remove meat and let rest 15 minutes.
Place vegetables in a bowl and cover. Add as much broth (cooking liquid reserved in the Dutch oven or large pot) as you want. Slice meat across the grain.
