Prepare the pie dough: Combine flour and salt in a bowl. 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, 1 tablespoon at a time, mixing until the dough just comes together. Divide into two slightly unequal discs, wrap in plastic, and chill for at least 1 hour.

Preheat oven to 400°F (200°C). On a lightly floured surface, roll out the larger dough disc and carefully place it into a standard 9-inch pie plate. Trim the edges, leaving a 1-inch overhang, and return to the refrigerator.

Make the filling: In a large bowl, gently toss the sliced nectarines with granulated sugar, brown sugar, cornstarch, vanilla bean seeds (or extract), and lemon juice until evenly coated.

Assemble the pie: Pour the nectarine mixture into the chilled bottom crust. Dot the top of the fruit with the small pieces of butter. Roll out the second piece of dough for the top crust. Place it over the filling, seal the edges by crimping the top and bottom crusts together, and cut several vents into the top to allow steam to escape.

Finish and Bake: Whisk the egg and milk together for the egg wash. Brush evenly over the top crust and sprinkle generously with turbinado sugar. Place the pie on a baking sheet (to catch drips) and bake at 400°F for 20 minutes. Reduce the temperature to 375°F (190°C) and continue baking for 45 to 50 minutes, or until the crust is golden brown and the filling is visibly bubbling thickly. If the edges brown too quickly, cover them loosely with aluminum foil.

Cool completely: Let the pie cool on a wire rack for at least 3-4 hours before slicing. This allows the fruit juices to fully set up, preventing a runny slice.