Make the Dough: In a large bowl, combine the all-purpose flour, granulated sugar, and salt. Add the cold butter pieces and use a pastry cutter or your fingers to work the butter into the flour mixture until it resembles coarse crumbs.
Add the Ice: Gradually add ice water, one tablespoon at a time, mixing until the dough just comes together. Be careful not to overwork the dough. Form the dough into a disc, wrap it in plastic wrap, and refrigerate for at least 30 minutes.
Prepare the Filling: While the dough is chilling, prepare the filling. In a medium bowl, combine the sliced peaches, granulated sugar, all-purpose flour, vanilla extract, and a pinch of salt. Gently toss the peaches to coat them evenly with the mixture.
Roll Out the Dough: Preheat your oven to 400°F (200°C). Remove the dough from the refrigerator and place it on a lightly floured surface. Roll the dough out into a circle, about 12 inches in diameter. Transfer the rolled dough to a parchment-lined baking sheet.
Assemble the Galette: Arrange the peach slices in the center of the dough, leaving a 2-inch border around the edges. Fold the edges of the dough over the peaches, pleating as you go to create a rustic crust. Brush the crust with milk or cream.
Bake the Galette: Bake the galette in the preheated oven for 35-40 minutes, or until the crust is golden brown and the peaches are tender and bubbling.
Finish and Serve: Remove the galette from the oven and let it cool slightly on the baking sheet. Dust the crust with powdered sugar before serving. Serve warm or at room temperature.