Preheat oven to 400℉.
To make the pie crust, in a medium bowl, mix together the flour, salt, and shortening with 2 forks or a pastry blender until it forms a coarse, pebble-like texture. Stir in the water (Editor's Note: Add water 1 tablespoon at a time mixing until all flour is moistened - do not over mix) until a dough forms and turn out onto waxed paper. Shape into a ball and place in refrigerator for 15 minutes to chill.
While the dough is chilling, make the filling. In a large pot over medium heat, melt the butter and sauté the onion, celery, carrots, and potato. Add the salt, pepper, thyme, and celery seed. Cook, stirring occasionally, until the onion is translucent, and veggies are tender.
Add the chicken, peas, and flour and stir continuously for 3 more minutes.
Stir in the chicken stock and bring the mixture to a boil. Stir often and cook at a low boil until thickened, about 5 minutes. Stir in the milk, and then turn off the heat and let mixture rest for 10 minutes.
To assemble the pot pie, divide the pie-crust dough ball into two even halves and place on a floured board or countertop. Roll out both halves to fit a 9-inch pie pan.
Fit the bottom pie crust into the pie pan. Scoop the chicken filling into the pie crust. Fit the top pie crust over the filling, and press together the edges to create a seal.
In a small bowl, whisk the egg. Brush the egg wash on top of pie crust to give a golden, crisp finish. Sprinkle with kosher salt, if desired. Cut a few vents in the top of the crust to allow steam to escape during baking.
Place the pot pie on a baking sheet and bake for 45 to 60 minutes, or until golden brown. Note: If the edges of pot pie become too brown before it is finished baking, cover with aluminum foil. Cool the pot pie for 20 minutes before serving