Place a rack in the center of the oven then preheat to 425 degrees. Line a 9" deep-dish pie pan with 1 pie crust then trim excess from around the edges. Brush entire surface with beaten egg and place the crust into the refrigerator while you prepare the filling.
In a large bowl, combine peaches, sugar, brown sugar, flour, cinnamon, nutmeg, and cornstarch. Gently toss the peaches until completely coated and the dry ingredients have been dissolved. Remove prepared pie crust from the refrigerator then pour the filling into the crust, mounding the peaches slightly in the center. If there is just a bit too much juice, spoon the excess out before adding the top crust. NOTE: We strongly recommend you weigh your einkorn flour, if possible, for better accuracy. If you don’t have a scale, fluff the flour with a fork before you measure it in a cup. NOTE: When working with fresh fruit, the amount of thickener you need depends on how ripe the fruit is. If you’re using super sweet, ripe fruit, increase the cornstarch by 1 or 2 Tbsp.
Roll out the top crust on a lightly-floured surface into a 10" circle. Cut the crust into 1" wide strips. Carefully arrange strips over the top of the filling to make a lattice pattern. If you don’t want to go through the work of a lattice crust, you can cover the pie with the entire circle of crust—just cut a few small holes in the top with a sharp paring knife. This will allow the stem to escape during baking.
Fold the edges of the top crust under the edge of the bottom crust and press them together. Decorate or flute the perimeter of the crust as desired, then brush the entire surface with remaining egg wash and sprinkle lightly with sugar.
Place pie dish onto a rimmed baking sheet just in case the filling bubbles over. Bake pie at 425 degrees for 15 minutes. Reduce heat to 350 degrees then bake for an additional 30 minutes. After 30 minutes, turn oven off and allow the pie to remain in the oven for an additional 30 minutes. Remove the pie and cool completely on a wire rack.