Stick a clove into each onion half; set aside. Place ham in a large stockpot. Add enough water to cover, and bring to a boil. Drain off water. Cover ham with water once more, add onions, and return to a boil. Reduce to a simmer and cook, partially covered, for 2 hours.
Add potatoes, carrots, parsnips, and turnips. Return to boil. Reduce to a simmer and cook, partially covered, until about three-quarters of the way done; this will take about 20 minutes (start checking 10 minutes after the liquid comes to a boil). Remove ham to carving board. Add cabbage to pot, and return to a boil. Cook, partially covered, until all the vegetables are tender when pierced with the tip of a knife, 5 to 10 minutes more.
Transfer vegetables to a large serving platter, and sprinkle with parsley. Slice ham and serve with vegetables. Serve with vinegar, mustard, and horseradish on the side.