Start by making the pie dough. In a food processor, add the flour, sugar, and salt, and mix until combined. Add cold cubed butter and blend until the butter and the flour mixture are combined.
Add ice water and mix for 10 seconds. Press the dough between your fingertips and if the dough comes together, it’s ready. If not, add another tablespoon of water.
Transfer the dough to a clean floured surface and gather the dough into a disk. Cut it in half, cover each dough disk with plastic wrap, and place in the fridge for at least an hour.
Make the peach pie filling. Drain the canned peaches from the liquids, and slice them into thick slices. In a large mixing bowl, add the peaches, salt, lemon juice, cinnamon, sugar, and vanilla extract, and mix with a spoon.
Sift the cornstarch into the filling and mix it until well combined.
Start with rolling out the first dough disk and line the pie pan with it. Make small holes with a fork and fill them out with the pie filling. Cut the second piece of dough with a pizza cutter into even ½ inch strips. Gently place about 5 strips over the pie filling. Fold back the second and the fourth strips and place another strip vertically. Fold the strips over the strips and repeat with the rest of the strips.
Freeze the pie for 20 minutes to prevent the dough from browning quickly. Preheat the oven to 220c (425f).
Mix one egg with a tablespoon of milk or cream and brush the top of the pie. Sprinkle brown sugar on top.
Bake in a 180c (350f) preheated oven for 50-60 minutes on the lower third rack of the oven.
Allow the pie to cool to room temperature to allow the filling to set for at least 2 hours, and then store it in the fridge until you serve.