Whisk together the flour, sugar, and salt in a large bowl. Cut in the cold butter with a pastry cutter until the mixture resembles coarse crumbs with pea-sized pieces of butter.
Add ice water one tablespoon at a time, mixing gently until the dough just comes together. Divide into two discs, wrap in plastic, and refrigerate for 30 minutes.
While the dough chills, combine the diced peaches, sugar, cornstarch, lemon juice, cinnamon, and salt in a medium saucepan. Cook over medium heat, stirring often, until the mixture thickens and the peaches soften, about 5-7 minutes.
Remove the filling from heat and stir in the vanilla extract. Let it cool to room temperature before assembling.
Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper. On a floured surface, roll one disc of dough to ⅛-inch thickness.
Use a 5-inch round cutter to cut out circles. Repeat with the second disc of dough, re-rolling scraps as needed.
Spoon 1 ½ to 2 tablespoons of cooled filling onto one half of each dough circle, leaving a ½-inch border. Fold the dough over to create a half-moon shape.
Press the edges together with your fingers, then crimp with the tines of a fork to seal. Cut two small slits in the top of each pie to vent steam.
Arrange the pies on the prepared baking sheet. Brush the tops with the egg wash and sprinkle with turbinado sugar.
Bake for 22-25 minutes, or until the crust is deep golden brown and the filling is bubbling through the slits. Transfer to a wire rack to cool.
Whisk together the powdered sugar, milk, and vanilla extract until smooth. Drizzle the glaze over the warm pies and let set for 10 minutes before serving.