This leg of lamb is cooked "en Gasconnade," or in the Gascon style, which in this case means a lot of garlic and oil-packed anchovies. The originality of the Gasconnade leg of lamb resides in the fact that the salt is provided by cured anchovies, and the morels in the sauce announce the change of season and celebrate spring.
Soak the morel mushrooms in cold water, then drain and let dry thoroughly. Heat the olive oil in a medium-sized skillet over medium-high heat. Add the morels and sauté for 2-3 minutes.
Reduce the heat, add the shallots and garlic, and cook until translucent. Add 4 tablespoons of the madeira to the pan, stirring constantly. Add the demi-glace, bay leaf, and thyme and simmer over low heat for 15-20 minutes.
In a small bowl, whisk together the cornstarch and remaining madeira. Add to the sauce and simmer for another 10 minutes. Remove the bay leaf and thyme. Set aside until ready to use.
Preheat the oven to 350 degrees.
Using a sharp knife, make 16 small incisions in the leg of lamb and slide the garlic halves into them. Make 12 small incisions between the fat and the flesh of the lamb and slide the anchovies into them. The anchovies should stay near the surface of the meat. Season with pepper, to taste.
Heat the duck fat over high heat in a heavy ovenproof pan large enough to hold the entire leg of lamb. Quickly sear the lamb on all sides then place the pan in the oven. Roast for 45 minutes, scatter the carrot, onion, and turnip around the roast and cook for another 40-45 minutes for medium-rare, or more, according to your preference.
Remove the meat from the oven and let it rest in a warm place. Discard the fat from the pan, deglaze with the duck demi-glace, and reduce by half over a high flame. Pass the sauce through a fine sieve, pushing on the vegetables to extract all of the juices. Return the sauce to the saucepan to warm. Slice the lamb and serve with the sauce on the side and with potatoes sautéed in duck fat.