For the dough

1. Whisk together the gluten-free flour, tapioca starch, sugar, and salt in a large bowl. Add the cold butter or coconut oil pieces. Using a pastry cutter or your fingertips, work the fat into the flour until the mixture resembles coarse crumbs with pea-sized bits remaining.
2. Drizzle in the ice water one tablespoon at a time, stirring with a fork until the dough just comes together and holds when pressed. Do not overwork it.
3. Form into a disc, wrap in plastic wrap, and refrigerate for at least 1 hour.

For the Filling

1. While the dough chills, place the apples, cane sugar, lemon juice, cinnamon, tapioca starch, and salt into a small saucepan. Cook over medium heat, stirring often, until the apples have softened, about 10 minutes. Remove from heat.

To Assemble

1. Preheat the oven to 375°F. Line a large rimmed baking sheet with parchment paper.
2. Turn the chilled dough out onto a piece of parchment sprinkled with tapioca starch. Place another piece of parchment on top, press to flatten, and roll out with a rolling pin. Using a 4½- to 5-inch round cutter (or lid), cut out 5 rounds of pastry. Transfer each round to the prepared baking sheet as you go. The dough may seem hard at first but softens as you work it — rolling out, cutting 2 rounds, then re-gathering and re-rolling works best. Don’t roll too thin, as the dough is delicate.
3. To transfer each round cleanly, use a metal spatula coated in tapioca starch; re-coat each time.
4. Place about 1½ tablespoons of apple filling just right of centre on each round. Coat your hands with extra tapioca starch and fold the pastry over the filling. Press to seal, pinching or pressing together any seams, then crimp with the tines of a fork.
5. In a small bowl, whisk together the egg and water. Brush the egg wash liberally over the tops and sides of each hand pie, especially over seams and cracks.
6. Bake for 20–22 minutes, until golden brown. Transfer to a wire cooling rack.
7. In a small bowl, whisk together the glaze ingredients. Add a little extra milk if too thick, or extra powdered sugar if too thin. Drizzle over the hand pies. Serve warm or at room temperature.
8. Store leftovers in an airtight container at room temperature for 1–2 days, or in the refrigerator for 3–4 days.