For the ribs, preheat the oven to 170C/325F/Gas 3.
Heat the oil in a large roasting tray over a medium to high heat. Add the beef ribs and fry, turning regularly, until browned on all sides.
Add the carrots, onion and garlic and stir until coated in the oil and pan juices.
Add the thyme sprigs, then pour in the chopped tomatoes, red wine and beef stock and mix well to combine. Bring the mixture to the boil, then transfer to the oven and cook, uncovered, for 2-2½ hours, or until the sauce has thickened and the meat is falling from the bones. Season, to taste, with salt and freshly ground black pepper.
Meanwhile, for the horseradish mash, boil the potatoes in a pan of salted water for 15-18 minutes, or until tender. Drain well then return to the pan.
Return the pan to the heat for a few seconds to drive off any excess moisture, then remove from the heat. Mash the potatoes until smooth using a potato masher or ricer, then beat in the butter and milk, using a wooden spoon.
Stir in the creamed horseradish until well combined, then season, to taste, with salt and freshly ground black pepper.
To serve, divide the beef ribs equally among four serving plates. Spoon over the cooked vegetables and sauce. Place a dollop of mash alongside each serving.