If you have trouble finding fresh quinces for this recipe, feel free to substitute pears.
Heat oven to 375 degrees. Have ready a 10-inch tart ring on a parchment-lined baking sheet. On a lightly floured surface, roll out dough into a 12-inch circle, about 1/8 inch thick. Place circle in tart ring; gently press dough into ring. Trim dough flush with top of ring.
Spread frangipane in an even layer on bottom of shell; chill shell 20 minutes.
In a large saucepan, combine sugar, wine, 2 cups water, star anise, and cinnamon; bring to a boil over medium-high heat. Reduce heat to a very low simmer; add quinces. Cover liquid with parchment paper. Cook until quinces are just tender, 30 to 40 minutes.
Using a slotted spoon, transfer poached fruit to a bowl; let cool. Remove anise and cinnamon from poaching liquid. Increase heat to high; reduce liquid until slightly thickened, about 20 minutes. Set aside to cool.
Slice poached fruit thinly crosswise. Arrange fruit in tart shell, stem ends in the center, fanning outward. Chill 20 minutes.
Bake until frangipane is brown and crust is golden, 35 to 40 minutes. Transfer tart to a wire rack to cool, 25 minutes. Remove tart ring, and let cool to room temperature.
When ready to serve, use a small brush to glaze fruit with reserved poaching liquid.