Preheat oven to 450. Prepare dough for bottom crust in 9-inch pie plate and place on a baking sheet lined with foil (to catch any juices that may boil over) set aside.
Fold blackberries, peaches, cornstarch, and sugar together in a bowl being careful not to break berries.
Pour the fruit mixture into the pie crust. Top with the other pie crust and crimp edges to seal. Cut three slits in the top of crust to vent. Sprinkle top of crust with cinnamon sugar.
Bake in preheated oven for 15 minutes. Reduce oven temperature to 350 and continue baking until top crust is golden and set, about 40 more minutes.
Allow pie to cool at least an hour or until it reaches room temperature (it's easier to slice at room temperature). Store leftovers covered in the refrigerator.
Serve with vanilla ice cream.