In a large heavy-bottomed pot, add the butter, parsnips, carrots, leek, onion, garlic, and celery and cook until just tender and the onions are slightly transparent. Once the vegetables are tender, stir in flour and make sure vegetables are well coated. Add broth, one cup at a time, mixing between additions. Bring to a slight boil and cook while constantly stirring for two minutes. Once the broth has become thick, stir in the heavy cream, parsley, salt, and pepper. Finally, mix in the shredded chicken, set aside, and allow to cool.
Roll out your two pie crust disks and place your bottom crust into a 9' pie dish. With the top disk, you can do a decorative design or just put it on top with a few ventilation slits and a crimped crust. Whisk the egg with a pinch of salt and set aside. I like to pop the crust in the freezer for about 15 minutes before adding the filling and baking. While your crust is chilling in the freezer, preheat the oven to 375°, placing a sheet pan on the middle oven rack, allowing it to preheat with your oven. Once the filling has cooled to a warm temperature, fill your chilled piecrust with pie filling and add the top crust. Brush the crust with the egg wash, sprinkle with flaky sea salt, and bake on the baking sheet for about 45 minutes to one hour. If your crust starts to brown too quickly, cover with foil. Let the pie cool for about 20 minutes before serving.