01 - Whisk together flour, salt, and sugar in a large bowl. Cut in cold butter using a pastry blender or two forks until mixture resembles coarse crumbs. Gradually add ice water, 1 tablespoon at a time, mixing until dough holds together. Divide into two disks, wrap in plastic, and refrigerate for at least 1 hour.
02 - Preheat the oven to 400°F.
03 - Toss sliced peaches with granulated sugar, brown sugar, cornstarch, cinnamon, nutmeg, salt, lemon juice, and vanilla in a large mixing bowl until well combined. Let sit for 10 minutes to draw out some juices.
04 - Roll out one disk of chilled dough on a floured surface to fit a 9-inch pie dish. Gently transfer to the dish, letting excess hang over the edges.
05 - Pour the peach filling into the pie crust, spreading evenly.
06 - Roll out the second dough disk for the top crust. Lay it on whole and cut slits for steam, or create a lattice pattern. Trim and crimp edges to seal.
07 - Brush the top crust with beaten egg and sprinkle with coarse sugar if desired.
08 - Place pie on a baking sheet to catch drips. Bake for 20 minutes at 400°F, then reduce oven temperature to 350°F and bake an additional 35-40 minutes, until crust is golden and filling is bubbling.
09 - Cool the pie on a wire rack for at least 2 hours before slicing to allow the filling to set.