Preheat your oven to 425°F (220°C).
Lightly grease a 9" pie pan that's at least 1 1/2" to 2" deep; if you use the shallower option, the pie will be more domed. To make the filling: In a large bowl, combine the apple slices, granulated sugar, cinnamon, nutmeg, salt, and tapioca flour until thoroughly mixed.
Combine the granulated sugar, all-purpose flour, and cinnamon, and spread this mixture evenly on the bottom of the rolled-out pie crust. This adds sweetness and spice while helping absorb extra moisture from the apples.
To assemble the pie: On a floured surface, roll out one disc of chilled pie dough until it forms a 12" circle. Place it into a 9-inch pie dish.
Spoon the prepared apple filling into the pie crust, piling it high and tightly.
Roll out the second disc of chilled pie dough into an 12-inch circle. Trim off any excess dough, fold the overhang back, and pinch the edges to seal. Crimp or flute as desired.
Brush the top crust with the egg wash and sprinkle with coarse sugar (if using). Place the pie onto a parchment-lined baking sheet and bake for 15 minutes. Keeping the pie in the oven, reduce the temperature to 375°F (190°C) and bake for another 45-50 minutes until the filling bubbles. When the pie is done — you should see the filling bubbling vigorously, either around the edges, or via any decorative vents — remove it from the oven.
Allow the pie to cool completely before slicing to ensure the filling sets properly. Cool pie all day (or overnight) before cutting.
Store any leftover pie, lightly covered, at room temperature for several days. Freeze for longer storage.