Preheat the oven to 350°F.
Score the outer fat of the lamb shoulder with the tip of the paring knife at 1 inch intervals, do not cut into the meat. In a small bowl, mix together the Dijon mustard, minced garlic, minced thyme, and extra virgin olive oil. Rub the mustard mixture into all of the interior surfaces of the lamb, but not on the exterior surfaces. Season the interior meat with kosher salt. Roll the lamb shoulder back together, then truss the lamb with butcher’s twine in ¾ inch intervals. Place the lamb back in the refrigerator and allow it to marinate overnight. The next day, remove the lamb from the refrigerator at least 2 hours prior to roasting to allow it to temper. Wipe away any excess marinade on the surface and pat the lamb dry with paper towels. Position the racks in your oven so the All-Clad TK 8 Qt. Rondeau can sit directly in the center.
After the lamb has tempered, season it liberally with kosher salt. Heat the All-Clad TK 8 Qt. Rondeau over medium high heat. Add the canola oil to the pan. When the oil is hot as indicated by a shimmering appearance on the oil’s surface and faint wisps of white smoke appear, carefully set the lamb in the oil with the outer fatty portion side down. Sear the lamb until it is golden brown, then carefully turn the lamb over to sear the other side. Continue to sear all surfaces of the lamb, then remove it from the rondeau and set it on a plate.
Carefully pour the hot fat out of the rondeau and return to medium high heat. Add 1 tablespoon of butter and the carrots, onions, turnips, and potatoes and season lightly with kosher salt. Allow the vegetables to lightly caramelize, stirring occasionally for about 5 minutes. Flatten the vegetables into an even layer, then return the lamb to the pan with the fat side facing up, on top of the vegetables. Place the rondeau in the oven.
Roast the lamb to an internal temperature of 132°F as checked with a meat thermometer. Remove the lamb from the oven and allow it to rest for at least 20 minutes. After resting, the internal temperature should rise to about 142°F. We do not recommend cooking lamb shoulder any less than this, as the meat will be chewy. After the resting period, move the roast to a carving board and loosely cover it with foil. Test the vegetables for tenderness; if the vegetables need more cooking, place the lid over the rondeau and set over medium heat for a few minutes. Heat the rondeau to reduce the juices and lightly glaze the vegetables. When the vegetables are tender, add the blanched peas, thyme leaves, and minced parsley.
When the peas are heated through, use a slotted spoon to transfer the vegetables to a serving dish, cover with foil, and keep warm. Pour out any remaining fat from the rondeau, then return to medium high heat and add the stock. Use a wooden spatula or spoon to scrape the caramelized solids from bottom of the pan. They should eventually dissolve in the stock. Reduce the liquid by about a half, then add the vinegar, whisk in the butter, and adjust the seasoning with salt. Strain the sauce through a fine mesh sieve into a serving dish and keep warm. Slice the lamb about one quarter inch thick across the grain. Lightly season the sliced lamb with coarse finishing salt and freshly ground black pepper. Serve immediately with the vegetables and sauce.