FILLING
If you choose to make the pie crust, start the recipe for the crust at least 2½ hours before the pie filling, or the day before.
To make the crust, combine the flour and salt in a large bowl. Add the butter cubes and combine with a fork until you have coarse crumbs. Add the water 1 tablespoon at a time, stirring with a wooden spoon, until the
dough forms a ball. Wrap the ball in plastic wrap and chill in the fridge for at least 4 hours or up to overnight.
If you're making the pie straight away, you can begin making the filling after 2½ hours (the filling takes about 1½ hours to prepare and cook, meaning that when it's finished, the pastry will have been in the fridge for 4 hours).
Preheat a sous vide water bath to 183°F/84°C.
Meanwhile, to make the filling, heat a large saucepan over medium heat and melt the butter. Stir in the flour until well combined, then add the sugars, cinnamon, salt, cider, and lemon juice and simmer until the mixture has reduced by half and becomes thick and syrupy, about 10 minutes. Pour the contents into a large resealable bag and add the sliced apples. Seal using the displacement method, clip the bag to the edge of the preheated water bath, and cook for 1 hour.
Toward the end of the sous vide cooking, preheat the oven to 375°F/190°C. Divide the pie crust in half and roll out on a lightly floured surface (about ½ inch/3 mm thick, 13 inches/33 cm in diameter).
Transfer it to a 9-inch/23-cm pie tin or dish and fit it inside. Roll out the second half in the same way. Slice into 34-inch/2-cm-thick strips to form a lattice over the filling. Brush the bottom pie crust with the egg white and pour in your apple filling. Form the lattice over the top with the strips. Paint the top crust with the egg wash and sprinkle with the granulated sugar.
Place the pie on a foil-lined baking sheet to catch any drips, transfer to the oven, and bake for 35 to 40 minutes, or until the crust is golden.