In a large mixing bowl, combine the flour, sugar, and salt. Add the cold, cubed butter and mix using a pastry cutter or your fingers until the mixture resembles coarse crumbs.

Gradually add the ice water, one tablespoon at a time, mixing until the dough just comes together. Divide the dough in half, shape each half into a disc, wrap in plastic wrap, and refrigerate for at least 1 hour.

Preheat your oven to 425°F (220°C).

After the dough has chilled, roll out one disc on a floured surface to fit your 9-inch pie dish. Place the rolled-out dough into the pie dish, trimming any excess dough hanging over the edges.

In a large bowl, combine the sliced peaches, sugar, cornstarch, lemon juice, and cinnamon. Toss until the peaches are evenly coated.

Pour the peach filling into the prepared pie crust. Dot the filling with small pieces of butter.

Roll out the second disc of dough and place it over the filling. You can create a lattice pattern or simply cover it completely. Trim any excess dough and crimp the edges to seal. Cut a few slits in the top crust for steam to escape.

Brush the top crust with the beaten egg to give it a nice golden color when baked.

Place the pie on a baking sheet to catch any drips and bake in the preheated oven for 45 minutes, or until the crust is golden brown and the filling is bubbly.

Once baked, remove from the oven and let the pie cool on a rack for at least 2 hours before slicing.