Prepare the Pie Crust:
In a large bowl, combine flour, salt, and sugar.
Cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs.
Slowly add ice-cold water, one tablespoon at a time, and mix until the dough starts to come together.
Divide the dough into two equal portions, flatten into discs, wrap in plastic wrap, and refrigerate for at least 1 hour.
Prepare the Peach Filling:
Drain the canned peaches and slice them if they are in halves.
In a large bowl, mix together the peaches, sugar, cornstarch, cinnamon, nutmeg (if using), lemon juice, and vanilla extract. Stir well until everything is combined.
Roll Out the Pie Dough:
Preheat your oven to 400°F (200°C).
Roll out one of the chilled dough discs on a lightly floured surface to about 1/8-inch thickness.
Carefully transfer the dough to a 9-inch pie dish, trimming any excess dough around the edges.
Pour the peach filling into the prepared pie crust, and dot the top with small pieces of butter.
Top the Pie:
Roll out the second disc of dough for the top crust. You can either lay it flat over the pie or create a lattice design by cutting strips.
Seal the edges of the pie and trim any excess. If using a flat top crust, make a few slits to allow steam to escape.
Add the Egg Wash:
In a small bowl, mix the beaten egg with milk.
Brush the egg wash over the top of the pie for a golden, shiny finish.
Bake the Pie:
Bake the pie in the preheated oven for 40-45 minutes, or until the crust is golden brown and the filling is bubbling.
If the crust browns too quickly, cover the edges with aluminum foil.
Cool and Serve:
Allow the pie to cool for at least 2 hours before slicing. This will help the filling set properly.
Serve with whipped cream or vanilla ice cream, if desired.