1 1/4 pounds quince, 2 large (peeled, cored and cut into 3/4-inch dice)
1 pound firm, crisp apples, such as Fuji or Granny Smith (peeled, cored and cut into 1-inch dice)
1/2 cup Sugar
1/3 cup finely minced crystallized ginger
2 tablespoons fresh lemon juice
1 cinnamon stick (3 inches long)
1 star anise pod (broken into several pieces)
3 whole cloves
1/4 cup apple cider or juice
  Sweet pastry crust (Sweet Pie Dough for a single 10-inch crust)
  Flour (for dusting the work surface)
8 tablespoons unsalted butter (softened)
1/2 cup powdered sugar
1/2 cup (packed) light brown sugar
2 large eggs (at room temperature)
1 teaspoon pure vanilla extract
1/4 cup unbleached all-purpose flour
1/8 teaspoon salt
  Vanilla ice cream or whipped cream (for serving, optional)