Step 1At least 2 hours and up to 2 days before you plan to bake the tart, cook the quince: Peel each quince, cut into quarters then slice out and discard the cores. Cut each quarter into four smaller wedges, then transfer all the wedges to a medium saucepan. Pour in the wine, sugar, vanilla bean, bay leaf, ginger, cinnamon, star anise and 3 cups water and bring to a simmer over medium-high heat, stirring to dissolve the sugar.
Step 2Cut out a round of parchment paper the same diameter as the inside of the pan and place over the fruit. Once the mixture begins boiling, reduce the heat to medium-low to maintain a bare simmer and cook, stirring the quince occasionally, until soft and rosy pink, about an hour and a half.
Step 3Discard the parchment paper, then gently lift the quince wedges out of the syrup with a slotted spoon or spider and transfer to a double-thick layer of paper towels to drain. Reserve the syrup in the pan.
Step 4Heat the oven to 375 degrees. Unfold the sheet of puff pastry and roll it with a rolling pin on a lightly-floured surface until 12 inches square and 3/16-inch thick. Cut a 12-inch-diameter circle from the pastry and transfer it to a parchment paper-lined baking sheet. Arrange the quince wedges evenly over the pastry, leaving a 1-inch border all around. Bake, rotating the pan front to back halfway through, until the pastry is golden brown on the bottom and crisp (it will look pale in and around the fruit wedges), about 1 hour. Remove the tart from the oven and let cool.
Step 5While the tart cools, bring the saucepan of reserved quince poaching liquid to a boil over medium-high heat. Cook until reduced to 1/2 cup. Remove the pan from the heat and, while the syrup is still hot, use a pastry brush to brush it evenly over just the fruit in the tart. Sprinkle the fruit lightly with turbinado sugar, if you like, and let cool to room temperature before serving.