Combine the flour, sugar, salt in the bowl of a food processor and pulse a few times to combine.
Scatter the butter and shortening over the top of the flour mixture and pulse until the mixture resembles coarse meal. Add the water a few tablespoons at a time and pulse until the dough just comes together. Remove the dough from the machine and lightly knead on a flat surface until it just comes together. Form into a disk, wrap in plastic wrap and refrigerate for at least 1 hour.
Preheat oven to 375 degrees F.
Combine peaches, sugars, cinnamon, ginger, nutmeg, peach eau de vie and cornstarch or tapioca in a large bowl and mix until well combined. Toss the blackberries with the cassis. Let sit for 10 minutes, then use a slotted spoon to spoon the berries into the peaches, and toss.
Divide the dough in half and roll each half out on a lightly floured surface to 13 to 14- inch round. Transfer 1 of the rounds into the bottom of a 9-inch deep-dish pie plate. Spoon the fruit into the crust using a slotted spoon. Add some of the juices that have accumulated in the bowl. Scatter the butter over the top. Roll up remaining dough on rolling pin and unroll atop peach mixture. Trim edges of both crusts to 3/4-inch overhang. Fold edges over; press to seal. Crimp edges. Cut 6 slits in top crust to allow steam to escape. Brush top of the pie with the cream and sprinkle with the turbinado sugar. Place the pie on a baking sheet and bake on the bottom rack of the oven until the crust is golden and juices bubble thickly through slits, covering edges of crust with foil if browning too quickly, about 1 hour 20 to 30 minutes, until the bottom crust is brown and the juices bubbling. Cool pie 3 hours.