How to Make It
Preheat oven to 325°F. Stir together salt, sugar, pepper, and fennel in a small bowl. Rub mixture all over lamb. Place lamb in a large Dutch oven or other ovenproof heavy-bottomed pot and carefully pour in boiling water. Cover, transfer to oven, and bake until lamb is very tender, 3 to 3½ hours.
Remove pot from oven and uncover. Increase oven temperature to 500°F. Stir brown sugar and ¼ cup of the vinegar into juices around the lamb and return to oven. Roast, uncovered, until lamb is browned and vinegar mixture begins to reduce, about 10 minutes, watching closely to prevent burning.
Transfer lamb to a rimmed baking sheet. Transfer pot to stovetop and bring vinegar mixture to a boil over medium-high. Cook, occasionally spooning off and discarding fat from surface, until sauce reduces, about 5 minutes. (There should be about ⅔ cup sauce.) Stir in remaining 1 tablespoon vinegar.
To serve, pull lamb shoulder apart into large pieces and place on a platter. Spoon sauce over top and garnish with parsley.