Combine flour, granulated sugar, ground cinnamon, and Kosher salt in the bowl of a food processor fitted with blade attachment. Add cold, cubed, unsalted butter and cold, cubed shortening. Pulse until pea-sized pieces form. Add ice water and pulse.
Remove the dough and wrap tightly in plastic wrap, pressing it down into a round, flat disc. Chill in a fridge.
Place sliced apples, brown sugar, lemon zest, fresh lemon juice, vanilla extract, cornstarch, ground cinnamon, and Kosher salt in a large bowl, then toss to thoroughly mix.
Line a rimmed baking sheet with parchment paper. Lightly flour a work surface, then use a rolling pin to roll the chilled dough out into a circle. Carefully roll the dough up around the rolling pin, then transfer it to the prepared baking sheet.
Use a slotted spoon to transfer the filling to the crust, allowing excess juice to drip off and leaving about 2-inches of dough overhang on all sides. Gently fold the edges of the dough up and over the filling, overlapping the dough every few inches as you go. Press down slightly to seal. Dollop.
In a small bowl, whisk together an egg and heavy cream, milk, or water, then use a silicone pastry brush to brush all over the pie dough. Sprinkle the pie dough with coarse turbinado sugar.
Transfer the pie to a freezer to chill. When ready, preheat an oven to 400F with a rack placed in the lower third of the oven.
Bake until the crust is golden brown and the filling is bubbling. Allow the galette to cool before carefully transferring to a wire rack. Serve with salted caramel and vanilla ice cream.