A day in advance, rinse the anchovies under cold running water; pat dry with paper towels. Cut the fillets in half lengthwise and place them in a small bowl with 3 tablespoons of the olive oil, garlic, and thyme. Let stand at room temperature, covered, for 2 to 3 hours.
Place the lamb shoulder, fat side down, on a work surface. Use a small knife to remove any tendons and hard cartilage. Make shallow slits in the meat about 1 inch apart. Remove the anchovies from the oil, reserving the oil, and stuff the fillets into the slits. Place any remaining anchovy pieces in creases between large portions of flesh. Roll the shoulder tightly into a sausage shape. Tie securely with butcher's string at 1½-inch intervals. Rub the roast with the reserved oil and wrap in plastic wrap. Refrigerate for 6 hours or overnight.
Heat the remaining 2 tablespoons olive oil in a large heavy skillet over moderately low heat until rippling. Add the lamb bones and sauté, turning occasionally, until well browned, about 15 minutes. Pour off the fat from the skillet; add ½ cup of the stock, scraping up brown bits that cling to the pan. Add the remaining 1½ cups stock; heat to boiling. Reduce the heat, partially cover, and simmer, skimming often, until about 1½ cups of rich broth develops, 1 to 2 hours. Strain through a fine-mesh sieve into a bowl; discard the bones. Let the lamb stock cool; refrigerate, covered, overnight. Scrape off any congealed fat before using.
About 2½ hours before serving, remove the lamb from refrigerator. Let stand for 1 hour to come to room temperature.
Preheat the oven to 500°F. Place the lamb on a rack in a flameproof roasting pan just large enough to hold it snugly. Roast in the top third of the oven for 15 minutes. Remove the lamb to a rack set over a plate to collect the juices; let rest for 30 to 45 minutes. Reduce the oven temperature to 425°F.
Meanwhile, skim the fat off the drippings in the roasting pan. Set the pan over moderate heat. Add the vinegar and bring to a boil, scraping up any brown bits that cling to the pan. Transfer to small heavy saucepan. Boil over moderate heat until reduced to 2 tablespoons. Whisk in the mustard and the reserved lamb stock. Add any juices that have accumulated under the roast. Set the sauce aside.
About half an hour before serving, return the lamb to the rack in the roasting pan. Roast until the thickest part of the lamb meat registers 135°F to 140°F for medium-rare, about 20 minutes. Transfer the roast to a carving board and let stand while finishing the sauce.
Degrease any roasting pan drippings and deglaze the roasting pan with 2 tablespoons water. Scrape into the sauce. Boil down to 1 cup, skimming. Season with salt and pepper to taste. Carve the lamb shoulder into ½-inch-thick slices. Arrange on heated plates. Spoon the sauce over and around lamb and serve.
If using salt-packed anchovies, rinse off the salt from 3 anchovies and divide into fillets. Soak in plenty of cold water for 2 hours; drain. Remove the fillets and cut in half lengthwise. Two and a half salt-packed anchovies equal 10 canned anchovy fillets packed in oil. If using the oil-packed fillets, simply rinse and blot dry.