On a lightly floured work surface, roll the puff pastry into an 11½-inch square, then cut out an 11-inch circle. Refrigerate the puffy pastry until ready to use.
In a medium cast-iron skillet (or other ovenproof nonstick skillet), combine the sugar, vinegar and water. Cook over medium heat, without stirring, until golden, 12 to 15 minutes. Stir in the butter, then arrange the pear wedges in a circle along the edge of the skillet. Reduce the heat to medium-low, and cook until the pears are crisp-tender, 10 to 15 minutes. Remove the skillet from the heat.
Drape the chilled puff pastry round over the pears, tucking the edges under. Place an oven-safe plate or pot lid on top of the pastry and bake for 15 minutes. Remove the lid and continue to bake until the puffy pastry is golden brown, about 15 minutes more. Allow the tart to cool in the skillet for 15 minutes, then run a knife around the edge of the skillet and carefully invert the tart onto a serving plate. Serve warm.