Preparation

Crust:

1. Insert the chopping blade in the work bowl of a Cuisinart® food processor.
2. Add the flour, granulated sugar, and salt, and process on Low to sift.
3. Add the cubed butter. Pulse until the mixture resembles coarse crumbs, 8 to 10 pulses.
4. Add the ice water, 1 tablespoon at a time. Pulse until the mixture just forms a dough (you may not need all the water). The dough is ready when it holds together when pinched.
5. Divide the dough into 2 equal pieces and form each into a flat disc.
6. Wrap each disc in plastic wrap and refrigerate for at least 30 minutes before using.
7. When ready to use, roll out both dough discs on a lightly floured surface to ⅛ -inch thick circles and fit into a 10-inch pie plate.
8. Chill in refrigerator for about 20 minutes.
9. While the dough is chilling, prepare the filling.

Filling:

1. In a small heatproof bowl, cover the dried cranberries with hot water, and soak until plump.
2. In a food processor fitted with the blade attachment, combine the sugars, arrowroot, cinnamon, nutmeg, allspice, and salt.
3. Pour the sugar mixture into a large bowl.
4. Add 1½ cups of the whole cranberries to the food processor fitted with the blade attachment, and pulse until roughly chopped.
5. Add the chopped cranberries and the remaining 1 ½ cups whole cranberries to the sugar mixture.
6. Insert the slicing disc into the work bowl of the food processor. Stand the apple halves upright in the feed tube and slice.
7. Transfer to the cranberry-sugar mixture, and add the lemon juice and vanilla. Toss gently.
8. Drain the dried cranberries, and add to the bowl with the rest of the filling. Toss gently.
9. Pour the filling into the refrigerated pie shell, and arrange the lattice or pastry round on top.
10. If making a lattice crust, cut the rolled pastry into ½ inch strips and arrange as desired.
11. If using full pastry round, cut vent holes into the pie dough. Crimp as desired.
12. Chill the pie in the refrigerator for 10 to 15 minutes.
13. Meanwhile, move an oven rack to the lowest position in the oven, and place a rimmed baking sheet on the rack.
14. Preheat the oven to 450°F.
15. Brush the top crust with the egg wash, and sprinkle with granulated sugar.
16. Place the pie on the rimmed baking sheet.
17. Bake for 15 minutes, or until the pastry is beginning to brown.
18. Lower the oven temperature to 350°F, and bake until golden-brown, another 30 to 35 minutes.
19. Allow to cool completely on a wire rack before cutting, 2 to 3 hours.