Combine flour, salt and sugar in a food processor; pulse it one time to mix. Add the butter pieces and pulse 4 times. Add shortening one tablespoon at a time and pulse each time you add a tablespoon. The mixture should resemble coarse cornmeal, with butter bits no bigger than peas.
Sprinkle 6 tablespoons of ice water over flour mixture one tablespoon at a time. Pulse once after you add each tablespoon of water. If you pinch some of the crumbly dough and it holds together, it’s ready. If the dough doesn’t hold together, keep adding water, a teaspoon at a time, pulsing once after each addition, until the mixture just begins to clump together.
Clean off your counter really well or use a pastry board or a nice cutting board. Flour your hands generously. Take the dough out of the food processor. Tilt the rolling pin and sprinkle it with flour as you rotate the rolling pin. Divide the dough into two balls and flatten each into a 4-inch wide disks. Sprinkle a little bit of flour on each disk and then wrap both separately in plastic wrap and refrigerate at least 1 hour before rolling.
When you are flattening the disks, you are not working the dough. You are just simply flattening the shape into a disk. Use the other pie disk for another pot pie.
While the dough is chilling, preheat oven to 375 F and prepare the filling.
Melt the butter in a large pot over medium-high heat, then add the onion, carrots, and celery. Cook until the onions turn translucent (about 3 minutes).
Stir in the turkey and sprinkle the flour over the top. Stir until it is combined with the turkey and vegetables. Stir and cook for about 2 minutes.
Pour in the chicken broth. Stir and let the sauce thicken. If you are using wine, add the white wine at this point.
Season with salt, pepper and thyme.
Add the cream and let it simmer for about 3 minutes. If sauce thickens too much, add a bit of the broth. Check the seasoning and add more salt and pepper to your taste.
Pour the filling into your skillet (I used a cast-iron skillet). Take the pie dough out of the refrigerator about 5 minutes before you need to use it. Roll out pie crust on a floured surface and place it over the filling. Press dough around the edges and against the side of the pan. Cut small vent lines on top of the dough.
Whisk together the egg with 2 tablespoons water and brush it all over the surface of the crust. There will be some wash remaining.
Place the pie on a baking sheet and bake for 25 to 30 minutes, until the crust is deep golden brown and the filling is bubbly. Check at 15 minutes. If the crust is starting to brown too quickly, lightly cover with foil paper for the remaining baking time.