Preheat the oven to 400°.
Cut the pie dough into 4 even pieces and form them into round balls. Place on a plate and cover, and chill.
Add 1 stick of butter to a large rondeau pot and cook the onions over low to medium heat for 15 to 20 minutes or until browned.
Stir in the carrots, celery, and garlic and sauté over medium heat for 4 to 5 minutes.
Deglaze with vermouth and cook until au sec, or almost gone.
Stir in the flour until combined to make a roux.
Pour in the chicken stock and turn the heat to high and stir until it becomes very thick.
Stir in the heavy whipping cream until combined.
Add the hominy, potatoes, turkey, peas, parsley, salt, and pepper, and mix. Cover with a lid and set aside.
Roll out each pie dough until it easily covers a 9” pie pan.
Take two of the rolled-out pie doughs and place one each into a 9” pan and form it to the sides of it, making sure it’s completely covered. It’s ok if there is quite a bit hanging over.
Evenly distribute the turkey pot pie filling between the two pie pans with pie dough and smooth it out.
Place the other two rolled-out pie doughs over top of each of the pie pans with filling.
Cut or tear off any excess pie dough around the outside and pinch the top and bottom pie dough together. Do this all the way around each pie to form the pie dough. You can also press the dough together using a fork.
Using a pastry brush, brush the top of the pie dough completely with a whisked egg.
Make a couple of slits in the dough using a knife so that air can escape.
Bake at 400° for 40 to 45 minutes or until the crust is golden brown.
Cool the pot pies for 10 minutes before serving.
