1. Preheat the oven to 140°C, gas mark 1. Pour the balsamic vinegar into a shallow bowl and roll the beef in it; season well. Heat half the oil in a deep ovenproof casserole over a medium-high heat and add the beef. Cook for 1-2 minutes on each side until browned all over; take care as the balsamic can burn easily. Remove from the pan, return to the vinegar bowl and set aside.
2. Heat the remaining oil in the pan over a medium heat and add the shallots, celery, carrots and parsnips. Sauté over a medium-high heat for 5 minutes until beginning to brown. Return the beef to the pan with the vinegar, garlic, thyme and stock. Season, then bring to the boil and cover with a tightly fitting lid. Transfer to the oven and cook for about 3 hours 30 minutes, or until meltingly tender, turning the beef and stirring the vegetables regularly.
3. Meanwhile, make the horseradish mash. Boil the potatoes in salted water for 10-12 minutes until tender, then drain. Return to the pan and allow to dry for 2 minutes, then mash with the butter, milk and horseradish. Season and add the parsley.
4. Remove the beef from the pan and wrap in foil to rest. Place the pan over a high heat and bring the gravy to the boil. Simmer briskly for 20-25 minutes until reduced by half; season. Slice or shred the beef and serve with the vegetables, gravy and horseradish mash.