Quince, a vibrant cousin of the apple, mingles well with spiced and sweet ingredients. The fruit is poached in a wine-spiked syrup, which coats it as it bakes.
Make the filling: Bring wine, water, granulated sugar, butter, cardamom, cinnamon sticks, ginger, and vanilla seeds and pod to a simmer in a large pot. Meanwhile, peel, core, and quarter quinces, adding them to pot as you work. Cover with parchment, and cook until quinces are soft and rosy pink, about 2 hours. Discard vanilla pod.
Preheat oven to 400 degrees. Make the crust: Roll out puff pastry to a 12-by-15-inch rectangle on a floured piece of parchment; transfer to a baking sheet. Freeze until firm, about 30 minutes.
Cut dough in half lengthwise to form two 6-by-15-inch rectangles. Using a slotted spoon, transfer quince onto puff pastry, leaving a 1-inch border. (There will be a small pool of liquid.) Brush border with egg wash. Top with remaining puff pastry, pressing edges to seal. Brush top with egg wash, and sprinkle with sanding sugar. Freeze until firm, about 15 minutes.
Cut six 2-inch slits every 2 inches along the top for steam vents. Bake until pastry is puffed and golden, about 45 minutes. Cut slab pie into triangular pieces. Serve immediately.