Preheat the oven to 375°F. Line a baking sheet with parchment paper.
To make the pastry crust, combine the flour, sugar, and salt in a large mixing bowl. Use a pastry cutter to cut the cold butter into the dry ingredients until the chunks of butter are about the size of peas. This can also be done in a food processor or using two knives if you don't have a pastry cutter.
1 1/2 cups (191g) all-purpose flour, 1 Tablespoon granulated sugar, 1/2 teaspoon table salt, 10 Tablespoons salted butter
Add the cold water a tablespoon at a time, stirring it in with a fork to evenly moisten the dough just until it starts to clump together. Gather the dough into a ball and flatten it into a disc on a piece of plastic wrap. Wrap it up and stick it in the fridge or freezer for 20 to 30 minutes. This serves both to keep the butter in the dough cold while also allowing the flour to hydrate from the water in the dough so it is easier to roll out.
4-6 Tablespoons ice water
Wash and slice the peaches into 1/2-inch slices. You can remove the peels if you like, but they soften considerably while baking so you won't notice them and they actually add to the rustic look of the galette, so I like to keep them. Add the sliced peaches to a large bowl with the sugar, cornstarch, cinnamon, and vanilla. Gently toss to evenly coat the peach slices. The sugar will start to draw out the juices from the peaches.
1 1/4 pounds peaches, 1/3 cup granulated sugar, 1 Tablespoon cornstarch, 1/4 teaspoon ground cinnamon, 1/2 teaspoon pure vanilla extract
Roll out the pastry crust on a lightly floured surface into a large 12-inch circle. Transfer to a baking sheet lined with a piece of parchment paper. You want it to hang over the edges a bit so you have crust to fold over the edges of the galette.
Arrange the peach slices in an overlapping circular pattern in the center of the crust, leaving about 1 1/2 to 2 inches border around the edges. I like to drizzle the sugary juices that came off the peaches over the filling unless there is a lot of it, in which case you might just want to discard it so the galette isn't overly runny.
Fold the edges of the crust over the peach filling, leaving the center open. Beat an egg with a little water and brush it over the edges of the crust, then sprinkle with coarse sanding sugar to finish.
1 large egg, 1-2 Tablespoons coarse sugar, 1 teaspoon cold water
Bake at 375°F for 45-55 minutes until the crust is golden brown and the peach filling is bubbling. Let cool for at least 15 minutes before slicing and serving warm or room temperature.