Preheat the oven to 400 degrees F (205 degrees C).
In a large bowl, combine the sliced apples and lemon juice, add the brown sugar, and mix well. In a small bowl, whisk together the granulated sugar, tapioca starch, cinnamon, nutmeg, and salt, making sure that the starch is evenly dispersed. Pour the sugar-spice mixture over the apples and toss to coat. Pour the filling into the bottom crust, making sure to scrape the entire contents from the sides of the bowl into the pie.
Top the pie with lattice strips and crimp the edges as desired. (You’ll have some extra dough to make Sugar Scraps). In a small bowl, beat the two tablespoons of white sugar into the egg, and brush the mixture over the top crust with a pastry brush, avoiding the crimped edges.
Use a crust protector, or gently wrap the crust’s edge with aluminum foil, to prevent it from burning. Place the pie on Holy Sheet to collect any juices that bubble over. Bake for 30 minutes, then reduce the heat to 375 degrees F (190 degrees C) and continue to bake for 40 minutes more, or until the filling has been bubbling for at least 10 minutes.
Transfer the pie to a cooling rack and cool for at least an hour before serving to make slicing and serving easier. (It will remain very juicy until it cools completely.) Serve warm or at room temperature. The pie will keep for up to three days at room temperature.