In a food processor, add flour, sugar, & salt. Pulse until ingredients are combined. Add shortening & pulse until mixture has a crumbly consistency. Add ice water, 1 tablespoon at a time, & pulse until dough just holds together. You may not need to use all of the water. Do not over process.
Form the dough into a disc & wrap in plastic wrap. Refrigerate for 10 minutes.
Remove the dough from the refrigerator & unwrap it. Roll dough to ⅛-inch thickness between two layers of lightly floured parchment paper. Using a sharp knife, cut the dough into a circle using a 9-inch round cake pan or plate for a template. Refrigerate the rolled out disc for 10 minutes.
In medium bowl, whisk together sugar, flour, & cinnamon. Add vanilla & peaches, & toss mixture until peaches are coated.
Preheat oven to 375 degrees F. Line a baking sheet with parchment paper. Remove the dough disc from the refrigerator & fan peaches, overlapping, in a circular shape in the center of the disc, leaving a 1-inch border. Fold the 1-inch border of dough over the edges of the peaches & refrigerate for 15 minutes.
Transfer unbaked galette to the prepared baking sheet, brush with maple syrup, & sprinkle with sugar. Bake for 30 to 35 minutes until the peaches look shriveled & crust is lightly browned. Let the galette cool for at least 5 minutes before serving. Serve & enjoy!