Put the peeled, sliced peaches in a bowl. Add granulated sugar and salt. Stir until the slices are coated. Cover and set aside for 30-60 minutes.
Drain and reserve the sweetened peach juice from the peach slices. Transfer the sliced peaches to a separate bowl and set aside.
Stir together the brown sugar, cornstarch, ground cinnamon, and ground nutmeg in a saucepan until combined.
Add the reserved peach juice and lemon juice and whisk until smooth.
Bring the sauce to a boil and then reduce heat. Simmer and stir until the sauce is thickened. Remove from heat.
Pour the sauce over the peach slices. Stir to coat.
Put one pie pastry into a 9-inch pie dish. Fill it with the peach pie filling.
Top with a second pie crust in either a lattice design or add the whole crust with slits cut into it for venting. Or see the notes for a crumb topping instead.
Brush with beaten egg white and sprinkle with sugar.
Bake at 450˚F for 10 minutes and then reduce the heat to 350˚F and bake for 45-50 minutes, or until the filling is bubbly. Cover edges loosely with foil or a pie shield halfway through baking if they are getting too brown.