Make the pie dough. Combine 2¼ cups (270g) flour, 2 tsp (8.4g) granulated sugar, ½ tsp ground cinnamon, and ½ tsp Kosher salt in the bowl of a food processor fitted with blade attachment. Add ½ cup (113g) cold, cubed, unsalted butter and 7 Tbsp (90g) cold, cubed shortening. Pulse until pea-sized pieces form. Add 3 Tbsp ice water and pulse. Add an additional tablespoon of water until the dough begins to form. 4 tablespoons is usually enough, but humidity and temperature can affect how much water is needed. Do not leave the motor running, simply pulse the dough until it holds together completely as one ball with no visible clumps.
Chill the pie dough. Remove the dough and wrap tightly in plastic wrap, pressing it down into a round, flat disc. Chill in a fridge for at least 30 minutes.
Make the filling. Place sliced apples, 5 Tbsp (62.5g) brown sugar, 1 tsp lemon zest, 1 Tbsp fresh lemon juice, 1 tsp vanilla extract, 2 tsp cornstarch, 1 tsp ground cinnamon, and ¼ tsp Kosher salt in a large bowl, then toss to thoroughly mix.
Roll out the dough. 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 approximately 13-inches in diameter. Carefully roll the dough up around the rolling pin, then transfer it to the prepared baking sheet.
Assemble the apple galette. 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 the top of the galette with 3 Tbsp cubed butter.
Brush with egg wash. In a small bowl, whisk together 1 large egg and 1 Tbsp of 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.
Chill before baking. Transfer the pie to a freezer to chill for at least 15 minutes or to a fridge for 30 minutes. When ready, preheat an oven to 400°F/205°C with a rack placed in the lower third of the oven.
Bake the galette. Bake for 40-45 minutes, or until the crust is golden brown and the filling is bubbling. Allow the galette to cool for 15 minutes before carefully transferring to a wire rack. Cool for an additional 30 minutes to allow the filling time to set. Slice, then serve with salted caramel and vanilla ice cream.