Using the dough blade or paddle attachment, combine the flour, sugar and salt in the bowl of a food processor or stand mixer. Pulse to ensure the mixture is evenly distributed.
Add the cubed butter and egg pulse a few times to break up the chunks, but there will still be some pieces of butter unblended. Add in the cold water and pulse until combined; it should form a rough dough.
Transfer the mixture onto a floured work surface and form the dough into a 1-inch thick disc using your hands. Wrap it tightly in plastic, and store in the fridge for 1 hour.
When ready to assemble and bake, preheat the oven to 400°F. Place the peaches, sugar, cornstarch and lemon juice in a large bowl and stir gently to combine. Set aside.
Remove the dough disc from the fridge and place on a lightly floured parchment paper. Use a rolling pin to roll the dough into about a 12-inch circle, about ⅛-inch in thickness. Transfer it with the parchment paper to a rimmed baking sheet.
Arrange the peaches on the flattened dough in a decorative pattern if desired, making sure to leave about a 2-inch border around the edge.
Fold the edges of the crust up and over the peaches, overlapping the edges as you fold. If you notice any cracks in the dough, you can use your fingertips to seal them.
Beat the egg and water in a small bowl. Brush the egg wash all over the top of the crust. Bake for 30-35 minutes, until the crust is golden and the peach juices begin to bubble.
Allow to rest for 15 minutes, then slice into 8 pieces and serve with vanilla ice cream if desired.
Tip: Avoid the microwave when reheating your peach galette to keep the crust crisp.