Prepare the Pastry: In a large bowl, whisk together the flour and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining. Gradually add ice water, one tablespoon at a time, mixing until the dough just comes together. Divide dough in half, flatten into discs, wrap in plastic, and refrigerate for at least 1 hour.

Prepare the Filling: In a separate large bowl, gently combine the halved strawberries and sliced nectarines. In a small bowl, whisk together the granulated sugar, cornstarch, lemon juice, and vanilla extract. Pour the sugar mixture over the fruit and toss gently until all the fruit is evenly coated. Set aside while you roll out the dough.

Assemble the Pie: Preheat your oven to 400°F (200°C). On a lightly floured surface, roll out one dough disc into a 12-inch circle. Carefully transfer the dough to a standard 9-inch pie plate. Trim and crimp the edges. Pour the fruit filling into the bottom crust, mounding it slightly in the center.

Top the Pie: Roll out the second dough disc. Cut vents in the top crust or create a lattice design. Place the top crust over the filling. Trim the edges, seal, and crimp them together with the bottom crust. Brush the top crust lightly with the beaten egg wash and sprinkle generously with coarse sugar.

Bake the Pie: Place the pie on a baking sheet (to catch any drips). Bake at 400°F (200°C) for 20 minutes. Reduce the oven temperature to 375°F (190°C) and continue baking for another 40-45 minutes, or until the crust is golden brown and the filling is visibly bubbling thickly. If the edges start to brown too quickly, cover them loosely with aluminum foil.

Cool and Serve: Let the pie cool completely on a wire rack for at least 3-4 hours before slicing. This allows the filling to set properly. Serve warm or at room temperature, perhaps with a scoop of vanilla bean ice cream.