Procedure

To make the crust

You can make the dough by hand or using a food processor.

By hand:
In a medium bowl, whisk together flour, sugar, and salt. Using a pastry cutter, cut shortening into flour until mixture has a crumbly consistency. Add ice water, 1 tablespoon at a time, and mix with a wooden spoon until dough just holds together. You may not need to use all of the water. Do not overwork.

Food processor
In a food processor, add flour, sugar, and salt. Pulse until ingredients are combined. Add shortening and pulse until mixture has a crumbly consistency. Add ice water, 1 tablespoon at a time, and 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 and wrap in plastic wrap. Refrigerate for 10 minutes.

Remove the dough from the refrigerator and unwrap it.  Roll dough to 1/8-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.

To make the filling

In medium bowl, whisk together sugar, flour, and cinnamon. Add vanilla and peaches, and toss mixture until peaches are coated.

To assemble and bake the Galette

Preheat oven to 375 degrees F. Line a baking sheet with parchment paper. Remove the dough disc from the refrigerator and 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 and refrigerate for 15 minutes.

Transfer unbaked galette to the prepared baking sheet, brush with maple syrup, and sprinkle with sugar. Bake for 30 to 35 minutes until the peaches look shriveled and crust is lightly browned. Let the galette cool for at least 5 minutes before serving.