Place the corned beef in a large pot or Dutch oven and cover with cold water. Cover the pot and bring to a boil, then reduce to a simmer. With a slotted spoon remove any scum that has risen to the surface.

Add the spice packet that came with the corned beef. Simmer approximately 50 minutes per pound or until fork tender. Remove the meat and cover loosely with foil to rest.

Add the whole potatoes and the carrots. Simmer until the vegetables are almost tender. Add the cabbage and cook for 15 more minutes.

Place the vegetables in a bowl and cover. Add as much broth (cooking liquid reserved in the Dutch oven or large pot) as you want. Slice the meat across the grain.