Preheat the oven to 200°C.
Layer vegetables and herbs in a roasting tin, place lamb on top, season, drizzle oil, and add stock.
Roast lamb uncovered for 30 minutes, then lower heat to 160°C, cover with foil, and cook for 4 hours.
Mix chopped mint, vinegar, and sugar in a bowl and set aside.
Boil potatoes in salted water, then simmer for 5 minutes.
Preheat beef dripping in a large tray in the oven.
Drain potatoes and shake to roughen the edges.
Coat potatoes in hot fat and roast for 30 minutes at 200°C, then turn and roast for 30 more minutes.
Remove tender lamb from juices and allow to rest while kept warm.
Set oven to 200°C for the parsnips.
Coat parsnips in sherry and honey, season, and roast for 20 minutes until golden.
Stir-fry cabbage in oil for 2 minutes, then finish with butter.
Shred lamb and serve with potatoes, parsnips, cabbage, mint sauce, gravy, and chestnuts.