Line 2 baking sheets with parchment paper and set aside. Preheat oven to 395°F (200°C).
Peel and coarsely grate the apples (I use a box grater). Transfer shredded apples to a sieve placed over a bowl, sprinkle with a tablespoon of sugar and let sit like that. Combine the rest of sugar, cornstarch, lemon zest and cinnamon in a medium bowl, set aside.
Flour your work surface, roll out your first sheet of puff pastry on top. Sprinkle it with flour, making sure you have no wet patches as this makes it easier to handle. Cut pastry into 4 equal strips then transfer them to the baking sheet. Brush the edges with a beaten egg.
Take the apples and fold them into the sugar mixture, mix until all apples are covered. Place about 2 spoonfuls of this onto one side of each pastry strip, leaving a border all around. If any juices flood the pastry, that's okay.
Fold the empty side of the dough over the filled side, seal the edges with a fork, brush each pie with egg and sprinkle with some turbinado sugar. Place in the center of the oven and bake for about 15 minutes until the pastry is puffy and golden brown in color. Remove from oven and let cool to room temperature before serving.
As the first batch bakes, repeat the process with the second sheet of pastry. Keep uneaten pies covered either at room temperature or in the refrigerator. You can also freeze them for up to 2 months.