Prep the oven and pan: Place a rimmed baking sheet on the center rack and preheat to 425°F (220°C). This helps crisp the bottom crust.
Roll the crust: Fit one crust into a 9-inch pie plate, letting the excess hang over the edge.
Keep the second crust chilled.
Make the filling: In a large bowl, combine peaches, granulated sugar, brown sugar, cornstarch, lemon juice, lemon zest, cinnamon, nutmeg, salt, and vanilla. Toss gently until evenly coated. Let sit 5 minutes to start releasing juices.
Fill the pie: Spoon the peach mixture into the bottom crust, mounding slightly in the center.
Dot with the butter pieces.
Top and seal: Place the second crust over the filling (or make a lattice). Trim excess, leaving about 1 inch overhang. Fold and crimp to seal.
Cut 4–6 small vents if using a full top crust.
Chill: Brush lightly with egg wash. Place the assembled pie in the fridge for 15–20 minutes to firm up. Mix the cinnamon sugar while you wait.
Bake hot, then lower: Set the pie on the preheated baking sheet.
Bake 20 minutes at 425°F, then reduce to 375°F (190°C) and bake 30–40 minutes more, until the crust is deep golden and the filling is bubbling vigorously through the vents.
Finish: In the last 10 minutes of baking, brush with a bit more egg wash if needed and sprinkle the cinnamon sugar evenly over the top. Bake until set and glossy.
Cool fully: Transfer to a rack and cool at least 3 hours before slicing so the filling can set.