Preheat the broiler.
Rub the leg of lamb all over with olive oil, about 3 tablespoons. Sprinkle the whole leg generously with salt and pepper. Wrap some foil around the tip of the bone, to prevent it from burning.
Place the lamb in a roasting pan fitted with a rack. Place the roasting pan in the oven and broil each side until golden brown, about 5 minutes on each side.
Remove the lamb from the oven and turn the oven to 325 degrees F. Loosely tent foil over the top of the whole lamb.
Return the lamb to the oven and cook to desired doneness, about 1 ½ hours for medium rare, or an internal temperature of 135 degrees F.
Rest the lamb for 10 to 15 minutes before slicing.