
Preheat the oven to 425F. Let the disks of pie dough warm up on the counter.
Meanwhile, score the bottom of each peach and peel the skin off. Halve the peaches, remove the pits, and cut them into ½-inch thick slices.
in a large bowl, mix gently to combine the peaches, sugar, cornstarch, lemon juice, vanilla, and cinnamon. Set aside while you roll the pie crust.
For the bottom crust, roll out 1 disk of pie dough into a 13-inch circle, about ⅛-inch thick. Press the dough into a 9-inch deep dish pie plate, leaving the excess to hang over the ends of the pie plate.
For the top crust, roll the other disk out into an 11-inch circle. Cut the dough into 1-inch-wide strips. (You should need 8 - 10 strips)
Place the peach mixture inside the bottom pie crust and smooth it out to create a level surface for the lattice. Dot the filling with the cubes of butter.
Arrange the pie crust strips in a lattice pattern over the fruit filling. Trim both the ends of the lattice strips and the excess bottom crust to have a 1-inch overhang from the edge of the pie dish. Fold the excess under itself and gently press down to create a flat edge. Crimp the edges with your fingers or a fork, if desired.
In a small bowl, beat the egg with 1 tablespoon of water. Brush the lattice topping and crust with the egg wash and sprinkle with about 1 tablespoon of coarse sugar.
Cover the edge of your pie loosely in aluminum foil. Bake for 20 minutes, then reduce the oven temperature to 375°F and bake for an additional 40 to 50 minutes, or until the top is golden brown and the filling is bubbling all over (even in the center!) If the pie starts to brown too quickly or reaches golden brown midway through baking, tent the whole pie with foil.
Place the pie on a cooling rack and cool for 4 to 5 hours before slicing.