Start by making the crust. Combine the flour, salt, and sugar in a food processor and pulse to mix. Add the cold butter and pulse 6–8 times. Add the cold water, a tablespoon at a time, until the mixture begins to clump together.
Remove the dough from the machine and place it in a mound on a clean surface. Divide it in half and gently flatten each half into a disk without over-kneading. Wrap each disk in cling film and refrigerate for at least 1 hour, ideally overnight.
Preheat the oven to 200°C.
To form the crust, remove one disk from the refrigerator and let it sit at room temperature for 5 minutes. Roll it out on a lightly floured surface into a 12–13-inch round, about 1⁄8 inch thick. Wrap the dough around a rolling pin and carefully unroll it over a 9-inch pie plate. Gently press the dough down so that it lines the bottom and sides of the tin, trimming any excess.
In a large bowl, combine sugar, flour and cinnamon. Add peaches and blueberries; toss to coat. Pour the filling evenly into the pie dish.
Remove the other disk of chilled pie dough from the refrigerator. Roll it into a 12-inch diameter circle. Cut 10 1.5-inch-wide strips using a pastry wheel, sharp knife, or pizza cutter. Weave the strips over and under each other on top of the filling, pressing the edges into the bottom crust to seal. Trim off any excess dough.
In a small bowl prepare the eggwash. Whisk together on egg with a tablespoon of water. Lightly brush the top of the pie crust with the egg wash and sprinkle with the demerara sugar.
Bake the pie in the oven for 20 minutes. Then, cover the edges of the pie pan with aluminum foil and bake for another 30 minutes or until the top is slightly golden.
Allow the pie to cool for at least 2 hours before serving. For best results, let it chill overnight.