In a large bowl, whisk together the whole wheat pastry flour and salt. Scatter the cold cubed butter over the flour and cut it in with a pastry blender or your fingertips until the mixture looks like coarse crumbs with pea-sized bits of butter still visible.
Drizzle in the ice water one tablespoon at a time, mixing gently, until the dough just holds together when pressed. You may not need all 8 tablespoons. Divide the dough into two discs, one slightly larger than the other, wrap each disc, and chill in the refrigerator for 1 hour.
Peel and thinly slice the 6 apples into even pieces about ¼ inch thick. Place the slices in a large bowl and toss with the lemon juice. Let them sit for about 10 minutes while the oven preheats, then drain off any liquid that collects.
To the drained apples, add the maple syrup, coconut sugar, arrowroot, cinnamon, nutmeg, cloves if using, vanilla, and a pinch of salt. Toss well until every slice is coated and no dry arrowroot remains.
Preheat the oven to 425°F (220°C). On a lightly floured sheet of parchment, roll the larger dough disc into a 12-inch (30cm) circle. Transfer it to the 9-inch pie dish and press it gently into the corners, leaving the overhang for now.
Pile the apple filling into the crust, mounding it slightly in the center. Roll the second disc into an 11-inch (28cm) circle and lay it over the top, or cut it into strips for a lattice. Trim the overhang to about 1 inch, then fold and crimp the edges to seal. Cut a few small vents in a solid top crust so steam can escape.
Brush the top crust all over with the beaten egg. Sprinkle the reserved 1 teaspoon coconut sugar evenly across the top for a light crackle.
Bake at 425°F (220°C) for 20 minutes. Reduce the oven to 375°F (190°C) and bake for another 30 minutes, until the crust is deep golden and the filling bubbles through the vents. If the edges brown too fast, cover them with a crust shield or strips of foil.
Transfer the pie to a wire rack and let it cool for at least 2 hours so the filling sets. Cutting too early gives you a runny slice, no matter how well it baked.