Preheat the oven to 375, and line a baking sheet with parchment paper.
On a well-floured surface, roll out half the dough into a circle, about 1/8 inch thick, using a bench scraper and additional flour as needed, to loosen the dough from the counter. Fit the dough into a deep-dish pie pan and trim the edge so there's about 1 inch of dough hanging over the edge of the pan.
Sprinkle the 1 tablespoon of flour over the bottom crust (to prevent a soggy crust), and pour the peach filling, including all the juices, into the crust. Dot the peach filling with the cubes of butter.
Roll out the other half of the dough into a circle, about 1/8 inch thick, using a bench scraper and additional flour as needed, to loosen the dough from the counter. You can either lay the crust over the top of the peaches, and cut a few slits to vent the steam, or cut into strips and arrange in a lattice design over the peaches. Gather up the scraps and re-roll to get all your lattice strips cut. Trim the edges of the lattice strips, then fold the edge of the bottom crust up and over, crimping it to make it look pretty.
Brush the top of the dough with the reserved egg white. If you like, sprinkle with 1-2 teaspoons extra granulated sugar for a sparkly finish.
Set the pan on the baking sheet. Bake on the center oven rack for about 90 minutes, until the juices are thick and bubbly in the center of the pie and bubbling over the edges. After about 30 minutes of baking, check to see if you need to cover the edges of the crust with a pie crust shield or strips of foil. After about 45-60 minutes of baking, once the top of the lattice crust is cooked through and golden brown, lay a piece of foil over the top to keep it from over-browning.Note: A browned crust on top does NOT mean the pie is done. You need to bake it until the juices in the middle are thick, with slow bubbles coming to the surface. This indicates that the corn starch has been activated and has properly thickened your pie filling, which can take the full 90 minutes.
Let the pie cool at room temperature for at least 2-3 hours. You can slice the pie while it's still warm, although it may be a bit messy. The filling will fully set after about 10-12 hours.