Dry Ingredients: In a food processor, pulse the flour, sugar, and salt until combined.
Butter: Add the cold cubed butter and pulse until the mixture looks like coarse crumbs.
Water: Add the ice water and pulse for 10 seconds. Squeeze a little dough between your fingers. If it holds together, it is ready. If not, add another tablespoon of water.
Chill: Gather the dough into a disk on a floured surface, cut it in half, wrap each piece in plastic wrap, and refrigerate for at least 1 hour.
Make the peach filling
Mix: Drain the canned peaches and cut them into thick slices. In a large bowl, stir together the peaches, salt, lemon juice, cinnamon, sugar, and vanilla extract.
Thicken: Sift the cornstarch over the filling and mix until well combined.
Assemble and bake
Line the Pan: Roll out the first dough disk and line the pie pan. Prick the bottom with a fork and add the peach filling.
Lattice: Cut the second dough disk into even ½-inch strips. Lay about 5 strips over the filling, fold back every other strip, and place one strip across. Unfold the strips, then repeat with the remaining strips to weave the lattice.
Freeze: Freeze the pie for 20 minutes so the crust holds its shape. Meanwhile, preheat your oven to 220°C (425°F).
Egg Wash: Beat the egg with 1 tablespoon of milk or cream, brush it over the lattice, and sprinkle with brown sugar.
Bake: Place the pie on the lower third rack, reduce the oven to 180°C (350°F), and bake for 50 to 60 minutes, until the crust is deep golden and the filling is bubbling.
Cool: Let the pie cool at room temperature for at least 2 hours so the filling can set before slicing.
Notes
Cold Butter: Cube the butter and chill it until you are ready to use it for the flakiest crust.
Don't Overwork the Dough: Pulse just until it comes together so the crust stays tender.
Chill the Dough: At least 1 hour in the fridge makes it easier to roll and helps it hold its shape.
Drain the Peaches: Drain the syrup completely so the filling isn't runny.
Fresh or Frozen Peaches: Use about 6 to 7 fresh peaches, or thawed and drained frozen peaches, and add 1 extra tablespoon of cornstarch.
Freeze Before Baking: 20 minutes in the freezer keeps the lattice sharp.
Lower Rack: Baking low in the oven crisps the bottom crust.
Protect the Edges: Cover the edges with foil if they brown too quickly.
Let It Set: Cool for at least 2 hours before slicing.
Storage: Keep at room temperature for 1 day or in the fridge for up to 4 days. Freeze the whole pie or slices for up to 3 months.