Instructions

1. Make the dough: In a small bowl, whisk together the cream, vanilla, salt, and egg yolk. In a food processor, blend the butter and confectioners sugar until creamy. Scrape down the bowl, then pour in the cream mixture and pulse until smooth. Add the flour and pulse until a dough just begins to form (do not ­overmix). Gather the dough into a ball, wrap in plastic, and gently press to form a disk. Refrigerate for at least 1 hour, or up to 3 days.
2. Poach the quinces: Using a vegetable peeler, remove four strips of lemon zest and add them to a large pot along with the lemon’s juice. Add the sugar, cinnamon stick, star anise, vanilla pod (not seeds), a pinch of salt, and 3¼ cups of water and bring to a simmer. Add the quince wedges, cover, and turn the heat to low. Simmer, turning the fruit occasionally, until the flesh is deep pink and soft when pierced with a knife, about 1½ hours. Cover and set aside until cool. (The cooled quince will keep in the liquid in the fridge for up to 1 week.)
3. Using tongs, transfer the quince to a cutting board and pat dry with paper towels. Place a fine-mesh strainer over a small pot and strain the cooking liquid, discarding the solids. Bring to a boil, then turn the heat to medium and simmer until the liquid has thickened and reduced by half, 30–45 minutes. Remove from the heat and set aside.
4. Meanwhile, using a sharp knife, core the quince wedges, discarding any hard and gritty bits. Cut each wedge crosswise into ¼-inch slices, keeping the sliced wedges together (do not separate the slices). Remove a couple of slices from the narrow ends of each segment so all the sliced wedges are about 3 inches long. (Reserve the scraps for another use.)
5. Make the frangipane: In the food ­processor, blend the butter, sugar, and a pinch of salt until light and fluffy. Add both flours, the almond extract, egg, and reserved vanilla seeds. Scrape down the bowl, then process until a thick paste forms. Cover and refrigerate until ready to use. (Frangipane will keep for up to 3 days in the fridge; set aside at room temperature until spreadable before using.)
6. Grease an 11-inch tart pan with nonstick spray. Between two large sheets of plastic wrap, roll the dough out to a 15-inch round, lifting the plastic occasionally to prevent creasing. (If the dough is too hard to roll, set aside at room ­temperature for 15 ­minutes; if it becomes too soft while rolling, refrigerate until firm.) Remove the top sheet of plastic, then ease the dough, exposed-side down, into the tart pan. Remove the plastic, then press the dough into the sides and corners of the pan. Using a knife, trim any overhang so the dough is flush with the top of the pan. Patch any cracks or thin areas with dough, then freeze for 30 minutes.
7. Position a rack in the center of the oven and preheat to 375°F. Place the pan on a baking sheet, then line the inside of the tart shell with a sheet of lightly greased foil. Fill with pie weights or dried beans, then bake until lightly browned at the edges, about 20 minutes. Remove the foil and weights and continue baking until the crust is dry and pale golden in the center, 6–8 minutes more. Transfer the tart to a wire rack and set aside to cool completely.
8. Turn the oven to 350°F. Scrape the frangipane into the crust and spread it evenly to the edges. Arrange the quince slices evenly atop the frangipane in a flower petal pattern.
9. Bake until the frangipane is puffed and deep golden brown, about 45 minutes. Transfer the tart pan to a wire rack and set aside for 10 minutes. Bring the reserved quince cooking liquid to a simmer, then brush it all over the tart. Set the tart aside to cool to room temperature, then unmold and cut it into wedges. (Loosely covered, the tart will keep in the fridge for up to 2 days.)