3 cups apple cider or apple juice
1 cup Sugar (divided)
  grated zest and juice of 1 lemon
1/2 teaspoon ground cinnamon
1/2 teaspoon ground allspice
1/2 teaspoon ground nutmeg
3 large quinces
2 cups blanched, slivered almonds
8 tablespoons unsalted butter (1 stick) (cut into 8 pieces, and at room temperature)
2 large eggs (at room temperature)
2 large egg whites
2 teaspoons pure almond extract
1 10 by 13-inch sheet of frozen puff pastry (thawed)
  Vanilla ice cream or crème fraîche (for serving, optional)