Preheat your oven to 375°F (190°C).
In a large mixing bowl, combine the drained sliced peaches, granulated sugar, brown sugar (if using), flour or cornstarch, cinnamon, nutmeg (if using), lemon juice, and vanilla extract. Mix gently until well combined.
Roll out one pie crust and place it into a 9-inch pie dish. Gently press it into the bottom and sides.
Pour the peach filling into the prepared crust and dot the top with pieces of butter.
Roll out the second crust and place it over the filling. Trim and crimp the edges to seal. Cut a few small slits in the top crust to allow steam to escape, or create a lattice top if desired.
In a small bowl, whisk together the egg and milk to make an egg wash. Brush it over the top crust and sprinkle with coarse sugar if using.
Bake for 30–35 minutes, or until the crust is golden brown and the filling is bubbling.
Remove from the oven and let the pie cool for at least 1 hour before slicing.