Make the crust by whisking together gluten free flour, sugar, and salt. Cut in cold butter using a pastry cutter or food processor until pea-sized pieces form. Drizzle in ice water and mix until dough just comes together. Divide in half, flatten into discs, wrap, and refrigerate for 1 hour.
Preheat oven to 400F. In a large bowl, toss sliced apples with sugar, cornstarch, cinnamon, nutmeg, and lemon juice until evenly coated.
Roll out one dough disc between parchment paper into a 12-inch round and fit it into a 9-inch pie dish, trimming any overhang. Fill with the apple mixture and dot the top with small pieces of butter.
Roll out the second dough disc and place it over the filling. Trim and crimp the edges together to seal. Cut 4 to 5 small slits in the top crust to vent steam.
Brush the top with beaten egg and sprinkle with coarse sugar. Place pie on a baking sheet and bake for 20 minutes at 400F, then reduce to 350F and bake 35 to 40 minutes more until golden and bubbly.
Let cool on a wire rack for at least 2 hours before slicing so the filling sets properly.