For the fruit: In a bowl, combine the peaches, sugar, flour, lemon juice and salt. Stir and set aside.
For the all-butter lemon pie crust: Combine the flour, salt and lemon zest in a large bowl. Add the butter and use a pastry cutter to gradually work it into the flour, until the mixture resembles tiny pebbles. This step should take 3 or 4 minutes.
Lightly beat the egg with a fork in a small bowl, then add it to the mixture. Next, add the cold water and vinegar and stir together until just combined.
Divide the dough into 2 halves, form the halves into dough balls and place each ball into a resealable plastic bag. Using a rolling pin, slightly flatten each ball of dough (to about 1/2 inch thick) to make rolling easier later. Seal the bags and chill for at least 20 minutes (or freeze if not using immediately).
Preheat the oven to 400 degrees F. Line a 9-by-13-inch baking sheet with parchment, overhanging the parchment 3 inches on opposite sides of the baking sheet to resemble a sling (so you can lift the pie out).
With a rolling pin on a lightly floured surface, begin rolling each piece of dough into a 9-by-13-inch rectangle. Roll the dough from the center outward. Be gentle and patient; it'll take a little time to get the dough completely rolled out.
Place one rectangle in the bottom of the prepared baking sheet. Spread out the fruit mixture evenly on top. Place the second crust on top of the fruit. Press and fold the edges together and crimp. Cut several vents in the top of the pastry in a flower pattern.
Bake until the crust is golden brown, about 1 hour 10 minutes. Cool for about an hour before lifting out and cutting.