Pre-heat the oven to 350 degrees F (177 degrees C).
Stir peaches with 1/2 cup of sugar and salt until well combined in a large mixing bowl. Let sit for 20-30 minutes. Strain the juices collected into a pan and return the strained peaches back to bowl.
Bring the juices to a rolling boil in a saucepan. Reduce heat to medium high and cook for 5-10 minutes until mixture becomes a thick syrup.
In a medium-sized bowl, whisk together 1/2 cup of sugar, flour and cornstarch. Mix lemon juice, cinnamon, cayenne, and pepper into peaches. Sprinkle flour mixture over and toss. Pour hot peach nectar over the peach mixture. Stir.
Roll one pastry out into a circle of 12 inches. In a 10 inch pie plate, press the bottom into place. Pour the peach filling in crust. Tap the pie plate on a flat surface, to help settle it, and then dot with butter.
Roll the remaining pastry into a circle of 11 inches and cut it into 1-inch wide strips with a paring blade or pastry wheel.
Spread 5 strips of pastry dough evenly on top of the pie. Continue weaving the remaining pastry strips to create a lattice-like top. Fold the lattice strips' ends under the bottom crust, and seal it with a crimp. Sprinkle 1 tablespoon of sugar and brush cream on top.
Bake for about 1 hour and 15 minutes in a preheated oven, until the crust is brown and the filling is bubbly. Let the cake cool completely before cutting.