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, to a ⅛-inch thick round (it should be 10-to 11-inch inches in diameter). If the dough cracks, just patch it up as needed (see how I do this in the video above!). Brush off any excess flour from the parchment paper, then slide the sheet of parchment (with the dough) onto a baking sheet.
Pile the strawberry filling onto the center of the dough and spread it in an even layer, leaving a 2-inch border. Fold up the edges of the dough, pressing them gently to seal. Refrigerate the galette for 10 minutes.
Whisk the egg with 1 teaspoon of water to make an egg wash. Brush the sides of the galette lightly with the egg wash (you won’t need it all). Sprinkle with the turbinado sugar. Dot the the strawberries with the butter. If your kitchen is warm, you can refrigerate the galette again for 5 minutes longer.
Bake the galette until the crust is deep golden brown and the filling is bubbling (a few of the strawberries will brown around the edges), rotating the pan halfway through, about 30-35 minutes. Place the baking sheet on a cooling rack. Using a pastry brush, brush some of the hot strawberry juices (from the center) over the top of the fruit—this will give the berries a bit of a shine. Let the galette cool.
Serve the galette slightly warm or at room temperature with a scoop of vanilla ice cream or a dollop of whipped cream, if you’d like.