Step 1
Preheat oven to 350 degrees F (175 degrees C).
Step 2
Stir peaches 1/2 cup sugar and salt together in a bowl. Let sit for 20 to 30 minutes. Strain accumulated juices into a saucepan and return strained peaches to bowl.
Step 3
Bring juices in saucepan to a boil; reduce heat to medium-high and cook until mixture thickens to a syrup 5 to 10 minutes.
Step 4
Whisk 1/2 cup sugar flour and cornstarch together in a bowl. Stir lemon juice cayenne pepper and cinnamon into peaches; add flour mixture and toss to coat. Pour peach syrup over peach mixture and stir.
Step 5
Roll out half the pastry to fit a 10-inch pie plate. Place bottom crust in pie plate. Pour peach filling into pie shell tap pie plate against a surface to settle filling and dot with butter.
Step 6
Roll remaining crust into an 11-inch circle and cut into 1-inch strips using a paring knife or pastry wheel.
Step 7
Lay 5 strips of pie crust over the top of the pie. Weave remaining pastry dough strips through to form a lattice top. Fold the ends of the lattice strips under the bottom crust and crimp the crust. Brush cream over the top and sprinkle with 1 tablespoon sugar.
Step 8
Bake in the preheated oven until browned and bubbling about 1 hour 15 minutes. Cool completely before slicing.