Preheat the oven to 180°C.
Rub oil into the lamb, season with salt and pepper, place in a tray with shallots and roast for 40 minutes.
Drain fat, add garlic and thyme sprigs, cover with foil, and bake at 120°C for 4.5 hours.
Pour red wine over the lamb and cook for one more hour.
Boil cubed potatoes in salted water until tender, then drain and mash them.
Simmer milk, butter, and chopped green onion tops for 4 minutes, then strain and reserve the liquid.
Mix the reserved milk liquid, egg yolk, and sliced white spring onions into the mashed potatoes.
Transfer the lamb, garlic, and shallots to a serving dish carefully.
Reduce cooking juices in a pan by one third, then whisk in cold butter and chopped thyme.
Serve the pulled lamb and shallots with champ mash and the red wine sauce.