Step 1Heat the oven to 400 degrees.
Step 2Place the lamb in a roasting dish and cook 50 minutes.
Step 3Remove the lamb from the oven to a large dish. Make 3 (5-inch) cuts down to the bone on each side, if using the shoulder, or 4 cuts to the bone through the meatiest part of the leg, and rub the cayenne and salt into the cuts. Let the meat sit in the dish 5 minutes and save the juices that drain.
Step 4Meanwhile, heat the grill to medium-high.
Step 5Grill the lamb and cook, turning once, until the meat at the bone is cooked medium-rare, 25 to 30 minutes, or until a meat thermometer registers 140 degrees. Remove from the grill and let sit 10 minutes.
Step 1Cut the mushrooms in quarters and place them in a skillet. Sprinkle generously with salt and cook, covered, over low heat, 10 minutes. They will release a thin juice. Drain, let the mushrooms cool and squeeze them out in a cloth.
Step 2Meanwhile, place the vinegar in a small skillet or saucepan with the cayenne, ginger and mace or nutmeg. Bring to a boil, reduce the heat and simmer 5 minutes.
Step 3Combine the mushrooms and the vinegar. (They can be used immediately or kept tightly covered for several months.) Mince half of the mushrooms. Place the mushrooms and the lamb juices from the plate into a skillet and cook over medium-high heat until sizzling hot. Serve with the lamb.