Pulse flour, salt, and sugar in a food processor. Add cold cubed butter and pulse until the mixture resembles coarse crumbs with pea-sized butter chunks. Add ice water one tablespoon at a time, pulsing until the dough just holds together. Divide into two discs, wrap in plastic, and refrigerate for at least 1 hour.
Blanch peaches in boiling water for 30-60 seconds, then transfer to an ice bath to peel easily. Slice the peaches into 1/4-inch thick pieces and place in a large bowl. Add sugar, cornstarch, lemon juice, lemon zest, cinnamon, nutmeg, and vanilla. Stir gently and let rest for 15-20 minutes.
Preheat the oven to 425°F (220°C) with a rack in the lower third. Roll out the first dough disc on a floured surface to a 12-inch circle. Transfer it to a 9-inch pie dish, gently pressing it into the bottom and sides without stretching. Refrigerate while rolling the top crust.
Roll out the second dough disc to a 12-inch circle and set aside. Remove the lined pie dish from the fridge and fill with the peach mixture, including any accumulated juices. Dot the filling with small pieces of butter, then cover with the top crust.
Trim excess dough leaving a 3/4-inch overhang, fold it under, and crimp the edges. Cut several vents in the top crust. Brush the crust with egg wash (egg mixed with milk) and sprinkle with turbinado sugar.
Place the pie on a rimmed baking sheet and bake at 425°F (220°C) for 20 minutes. Reduce oven temperature to 375°F (190°C) and bake for 35-45 more minutes until the crust is golden brown and the filling is bubbling through the vents. Tent edges with foil if they brown too quickly.
Transfer the pie to a wire cooling rack and cool for at least 3 hours before slicing. This allows the filling to set properly for clean slices.