Preheat oven to 375 degrees. On a lightly floured work surface, roll puff pastry to an 11 1/2-inch square; using a plate as a guide, cut out an 11-inch round. Refrigerate until ready to use.
In a medium cast-iron or ovenproof nonstick skillet, combine sugar, vinegar, and 2 tablespoons water. Cook over medium heat, without stirring, until golden, 12 to 15 minutes. Stir in butter. Arrange pear wedges in a circle along the edge of skillet. Reduce heat to medium-low, and cook until pears are crisp-tender, 10 to 15 minutes. Remove skillet from heat.
Drape chilled pastry round over pears, tucking edge under. Place a small oven-safe plate or pot lid on top of pastry; bake 15 minutes. Remove plate; continue to bake until pastry is golden brown, about 15 minutes more. Let tart cool in skillet, 15 minutes. Run a knife around edge of skillet, and carefully invert tart onto a serving plate. Serve warm.
For ease, use a melon baller or teaspoon to scoop out the pears' cores.