Sprinkle a large sheet of parchment paper lightly with flour. Roll out the dough on the parchment, lifting the dough and lightly flouring the parchment as needed to prevent sticking. You're aiming for a 10- to 11-inch round (it should be about ⅛-inch thick). If the dough cracks, just patch it up as needed. Brush off any excess flour from the parchment paper, then slide the sheet of parchment (with the dough) onto a baking sheet.
Pile the apple filling onto the center of the dough, then spread the apples in an even layer, leaving a 1- to 2-inch border. Fold the dough up over the apples, overlapping it and pinching it together (patch up any tears as needed). Refrigerate the galette for 5-10 minutes.
Beat the egg in a small bowl with the water. Brush the crust lightly with the egg wash (you won’t need it all), and sprinkle the crust with turbinado sugar. Dot the butter over the apples. If your kitchen is warm, pop the galette back into the fridge for a few minutes to chill (you want the dough to feel cool to the touch).