In a pan over low heat, cook the diced apples with brown sugar, lemon juice, vanilla, cinnamon, and cloves.
Stir occasionally and let cook for around 15 minutes, until the apples are tender but still hold their shape. Let mixture cool.
In a bowl, combine the flour, salt, shortening, sugar, and butter.
Cut the mixture together with a pastry cutter or forks until the butter breaks down into pea-sized pieces. Dough will still be crumbly.
Add cold water a tablespoon at a time, cutting it into the dough. Stop once the dough holds together when pressed.
Wrap in plastic wrap and chill for at least 1 hour, or overnight.
Preheat oven to 375°F and line a baking sheet with parchment paper. S
Split chilled dough into 8 even portions.
Roll each portion into a ¼-inch thick circle. Spoon about two tablespoons of the apple filling into the center.
Fold dough over and press the edges together with a fork.
Brush the tops with egg white and sprinkle with turbinado sugar, if using. Bake for 20–25 minutes.