Make the dough: Fill a liquid measuring cup with water and a few pieces of ice, and place in the freezer briefly. In a large bowl, add the flour, sugar, and salt, and stir briefly to combine. Add the cold butter pieces and, using your fingers or a pastry blender, smush them into the flour mixture until only pea-size pieces remain.
Retrieve the ice-cold water and drizzle 3 tablespoons of the liquid (no ice) into the flour mixture, working it in with your spare hand. Continue to add up to 3 tablespoons more water as needed, working it in until the dough is still crumbly but just moist enough to hold together when squeezed.
Place a large piece of plastic wrap on a work surface. Add half the dough (about 11 ounces) onto the plastic wrap, and press it to form a neat pile in the center. Using the sides of the plastic wrap and the warmth and force of your hands, firmly gather the dough into a tight ball, then flatten it into a compact, tightly wrapped 1-inch-thick disk with no visible cracks. Seal the dough tightly with a second piece of plastic wrap and refrigerate. Repeat with the remaining dough. Let the rounds chill for at least 1 hour and up to 1 day.
When ready to bake, remove one of the disks of dough to a well-floured work surface, and let it rest at room temperature for about 5 minutes, or until still chilled but more pliable. Using a lightly floured rolling pin, roll out the disk into a ⅛-inch-thick round, rotating often and flouring the surface more as needed to prevent sticking. Carefully transfer to a 9-inch glass or ceramic pie plate, and press it gently against the sides and bottom to fit. (Patch any holes as needed.) Refrigerate.
Roll out the remaining disk of dough using the same method, and transfer to a large, parchment-paper-lined baking sheet lightly dusted with flour. Cut lengthwise into seven 11⁄2-inch-thick strips. Refrigerate.
Set a rack in the lower third of the oven and preheat to 425°F. Line a rimmed baking sheet with foil, and set it aside. Meanwhile, prepare the filling: Gently pit the cherries, recruiting help as needed, and place them in a large bowl as you work. Stir in the sugar, tapioca flour, vanilla, lemon zest, cinnamon, and salt to distribute evenly. Working quickly so the cherries don’t release too much juice, retrieve the dough-lined pie plate and dough strips. Add the cherries and about ¼ cup of their juices to the center of the pie plate, mounding them slightly in the center. Weave the dough strips over the top in a lattice structure. Trim all but about 1½ inches of the overhanging top and bottom doughs, and discard. Roll up the remaining bottom dough over the top dough, and crimp the crust into your desired style. Transfer the pie to the freezer for 10 minutes.
Remove from the freezer, and transfer to the lined baking sheet. In a small bowl, beat the egg with 1 teaspoon cold water. Using a pastry brush, lightly coat the top and edges of the dough with the egg wash, and sprinkle the top dough with the remaining 2 teaspoons sugar. Bake in the lower third of the oven until the edges start to brown lightly, about 25 minutes. Lower the heat to 375°F, and continue baking, turning once halfway through, until the crust is golden brown and the filling looks thickened and syrupy and is bubbling slowly, 45–50 minutes more.
Remove the pie from the baking sheet and transfer to a wire rack. Let cool completely (or nearly) before slicing into wedges. Serve the slices with vanilla ice cream.