CRUST: In a large bowl, combine 2 cups flour and salt. Cut in shortening until mixture resembles coarse crumbs. Stir in ice cold water, form into a ball. Split into two balls; wrap each in plastic and refrigerate until ready to use.
FILLING: In a large saucepan, combine chicken or turkey cubes, carrots, peas, and celery. Add water to cover and boil for 15 minutes. Remove from heat, drain, and set aside.
In a saucepan over medium heat, cook onions in butter until soft and translucent. Stir in 1/3 cup flour, salt, pepper, and celery seed. Slowly stir in chicken broth and milk. Simmer over medium-low heat until thick, stirring occasionally. Remove from heat and set aside.
Preheat oven to 375 degrees.
Remove dough from the refrigerator. On a well floured surface, gently roll out each ball to fit a 9-inch pie plate. Place one of the crusts in the pie plate and press evenly into the plate's bottom and sides. Using a fork, prick holes in the bottom of the pie shell.
Pour the chicken or turkey and vegetable mixture into the bottom of the lined pie plate. Pour the hot cream mixture over all. Cover with the second pie crust, seal edges, and cut away excess dough. Make several small slits in the top to allow steam to escape. Optional: brush with egg wash, milk, or heavy cream.
Bake in the preheated oven for 30 to 35 minutes, or until pastry is golden brown. Cool for 10 minutes before serving.