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.
Add cheese: Add shredded cheese and toss together until combined.
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.
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 if you're slicing them now.
Filling
Arrange filling: Sprinkle the shredded cheese in the middle of the dough. Slightly fan out the apple slices and arrange them on top of the cheese, leaving about 2" of empty space around the edges of the dough.
Thyme butter: Melt the butter, thyme, and salt in a small bowl in the microwave or on the stovetop. Use a pastry brush to brush a thin layer on top of the apple slices. You may not need all of the butter but I like to get all of the thyme on the apples.
Create crust: Fold the outer edges of the dough over the apples, overlapping where needed. Place the entire baking tray in the fridge to let the dough chill and firm up any softened butter while the oven preheats.
Preheat: Preheat the oven to 350°F.
Egg wash: Right before baking, use a pastry brush to apply a thin layer of egg wash on the dough.
Bake: Bake 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. Serve warm or reheat individual slices before eating.