Step 1Heat the oven to 450 degrees. Using a sharp paring knife, cut thin slits all over the lamb and slide the slivers of garlic in. Season on all sides with salt and pepper. Set on a rack in a roasting pan. Rub the mustard all over the exposed surface.
Step 2Roast the lamb 10 minutes. Reduce the heat to 350 degrees and roast 1 1/4 to 1 1/2 hours, until cooked to desired doneness. Check after the first hour at lower temperature, using an instant-read thermometer inserted only into the meat, avoiding the bone. A reading of 120 degrees will be rare, 130 medium-rare, 140 for medium; the meat will continue to cook as it sits. Transfer to a carving board and let stand 20 minutes before carving.
Step 3While the lamb roasts, place the mint in a deep bowl. Combine the sugar with 1/4 cup of balsamic vinegar and 1 tablespoon of white wine vinegar in a small nonreactive saucepan with 1/4 cup water. Heat over medium-low heat until the sugar dissolves, 2 to 3 minutes. Immediately pour over the mint and toss well. Taste and add more sugar or vinegar as needed; the flavor should be sharply minty and sweetly balanced.
Step 4To serve, slice the lamb into serving portions and pass the sauce separately to be used judiciously.