Whisk together the flour, sugar, and salt in a large bowl.
Cut cold butter into the flour mixture using a pastry blender until coarse crumbs form with pea-sized butter pieces visible.
Add ice water one tablespoon at a time, tossing with a fork until the dough holds together when pressed.
Gather the dough into a disk on a lightly floured surface, wrap in plastic, and refrigerate for at least 30 minutes.
Combine sliced peaches, blackberries, sugar, cornstarch, lemon juice, cinnamon, and salt in a medium bowl.
Toss gently until the fruit is coated and no dry cornstarch remains, then let sit while you roll out the dough.
On a lightly floured surface, roll the chilled dough into a rough 12-inch circle about ¼-inch thick.
Transfer the rolled dough to a parchment-lined baking sheet and preheat the oven to 400°F (200°C).
Spoon the fruit filling into the center of the dough, leaving a 2-inch bare border around the edge.
Fold the bare edge of the dough up and over the fruit, overlapping every few inches to form loose pleats.
Brush the folded dough edges evenly with the beaten egg wash.
Sprinkle the turbinado sugar over the egg-washed crust for a crisp, sparkling finish.
Bake for 40 to 45 minutes until the crust is deeply golden brown and the fruit filling is bubbling thickly in the center.
Let the galette cool on the baking sheet for 15-20 minutes before slicing into wedges.