Cut butter into flour: In a large mixing bowl, stir together flour and salt. Add the cold butter and toss to coat in the flour. Press the butter in between your fingers to break them down into small, pea-sized pieces, tossing to coat in the flour occasionally.
Hydrate the dough: Make a well in the middle of the flour mixture. Pour in ice-cold water and mix together until it becomes a shaggy dough.
Fold dough: Turn the dough out onto a sheet of plastic wrap. Press the dough together with your hands and roughly fold it onto itself 2-3 times with your hands or a bench scraper until there aren't many dry patches left.
Chill dough: Shape the dough into a flattened disc shape and wrap it in plastic wrap. Chill the dough in the fridge for at least 3 hours or preferably overnight.
Cranberry Filling
Cook: In a small pot, add cranberries, sugar, and water. Cover and bring it to a boil on medium-high heat. Be careful as the cranberries will pop as they cook. When the popping subsides, uncover and continue cooking until most of the water has evaporated and it becomes a thick, jammy cranberry paste. Remove from heat and transfer to a bowl to cool completely before using it.
Prep: Line a baking sheet with parchment paper and set aside.
Roll out dough: On a floured surface, roll your chilled pie dough in a rough circle until it's about ⅛" thick, lifting and turning the dough occasionally to prevent it from sticking to the counter. Transfer the dough to your lined baking sheet and let it chill in the fridge while you prepare the apples.
Apple Filling
Mix: In a large bowl, toss together the apple slices, brown sugar, cinnamon, and cornstarch until the apples are coated. Sort the apple slices back into clusters of similar size and shape like they were when you were slicing them.
Add cranberry filling: Spread the cooled cranberry filling in the middle of the pie dough, leaving about 1-2" of the edge empty.
Add apple filling: Arrange the clusters of apple slices on top of the cranberry filling, alternating the orientation of each cluster.
Create crust: Fold the edges of the pie crust over the filling, overlapping as needed.
Apply egg wash: Use a pastry brush to brush the dough with a beaten egg. Sprinkle sugar crystals or coarse sugar on top of the egg wash.
Chill & preheat: Place the whole baking sheet with the galette in the fridge to chill while you preheat the oven to 350°F. Chilling the galette before baking will help any softened butter firm up for flaky layers and help the crust keep its shape.
Bake: Bake the galette for 45-55 minutes or until the crust is golden brown and the filling is bubbling. Let the galette cool on the baking sheet for at least 30-60 minutes or until the bottom of the pan is cool enough to touch with your bare hand. Serve warm with ice cream and sugared cranberries.