Cook's Note: You can increase the amount of sugar to 1 1/4 cups, depending upon the sweetness of the peaches. Peak summer peaches will only need 1 cup.
For the crust: In a food processor, combine the flour, sugar, salt and cold butter.
Pulse the processor until the mixture resembles fine sand. Remove the lid and add the ice water to the mixture. Run the processor just until the mixture rolls itself into a little ball. If the mixture is a bit dry, add more ice water by the tablespoonful until it comes together. Gather the dough into a ball. With a bench scraper or knife, divide the mixture evenly in half. Shape each half into a disk. Wrap each disk in plastic wrap and chill at least 30 minutes. At this point you can keep the wrapped dough in the refrigerator for a few days or freeze for later use.
Preheat the oven to 450 degrees F.
Flour your rolling pin and roll out 1 pie crust to about a 12-inch round and drape over a 9 1/2-inch fluted pie plate. Roll out the other pie crust to about a 10-inch round, and cut this into 1-inch strips with a fluted pizza cutter.
For the filling: Peel and cut the peaches into 1/4-inch thick slices (you should have about 7 cups) and toss with the lemon juice and almond extract in a large bowl. Whisk the flour, sugar, cinnamon, nutmeg and salt in another bowl, making sure there are no lumps. Stir the flour mixture into the peaches and mix well. Pour the peaches into the pie crust. Scatter with the pieces of butter. Top with the lattice strips. Brush away any flour underneath the lattice to make sure it seals well. Crimp the edges to seal. Beat the egg with 1 teaspoon water and brush the lattice and edges with the egg wash.
Pop in the oven and bake for 10 minutes, and then lower the heat to 350 degrees F and bake until the crust gets brown, about 50 minutes more. If the edges brown too fast, cover them with strips of aluminum foil about halfway through baking. Cool about 30 minutes before serving.