For the chicken: Start by putting the chicken in a pot and covering it with water. Bring the water to a boil, and then reduce the heat to low. Simmer for 45 minutes, and then remove the chicken from the pot. Set the chicken aside to cool briefly.
Shred the chicken with 2 forks, reserving the bones. For the stock, return the bones to the pot and boil for 20 minutes. Remove the bones from the pot and discard.
For the pot pie: When you're ready to use the Thyme Pastry, remove from the freezer and allow it to sit on the counter to thaw slightly, about 20 minutes. Preheat the oven to 400 degrees F.
Begin by finely dicing the vegetables. Slice the celery stalks into narrow strips, then slice in the other direction to create a fine dice. Repeat this process with the carrots, and the onion.
Melt the butter in a large pot or Dutch oven over medium heat. Add the onion, carrots and celery. Saute until the vegetables start to turn translucent, a couple of minutes.
Add 2 cups of the shredded chicken and stir to combine. Sprinkle the flour evenly over the vegetables and chicken, and stir to combine. Cook for a couple of minutes, stirring gently.
Pour in the chicken broth, stirring constantly. Stir in the bouillon cube and wine if using. The flour will combine with the chicken to create a delicious gravy. Next, add the peas.
Pour in the cream and stir. Allow the mixture to cook over low heat, thickening gradually, about 4 minutes. Season with the thyme, salt and pepper, and remove from the heat. Taste and adjust the seasonings as needed. Be sure it's adequately salted!
Pour the chicken mixture into a deep pie pan or small casserole dish.
Roll out the pastry so that it's 1 inch larger than the pan. Place the crust on top of the chicken mixture and cut small slits in the top. Press the crust gently into the sides of the dish to seal. I don't worry about making a perfect edge on my chicken pot pie because a) it looks more rustic and b) I'm lazy, hungry and I want to eat.
Bake until the crust is golden brown and the filling is bubbly, about 30 minutes. Cool for 10 minutes before serving.
To freeze: Allow the filling to cool completely then top with the crust. Cover with plastic wrap or aluminum foil and place in the freezer.
To cook from frozen: Remove the pot pie from the freezer, brush with egg wash (1 egg mixed with 2 tablespoons water or cream) and place directly in a 375-degree F oven and bake until lightly browned and bubbly, 30 to 45 minutes.
For the thyme pastry: Combine the flour and salt in a large bowl. Using pastry cutter, gradually work the butter into the flour until the mixture resembles tiny pebbles. This step should take 3 or 4 minutes.
Lightly beat the egg with a fork, and then add it to the mixture. Next, add in the cold water and vinegar. Stir the mixture together until it's just combined, and then remove half the dough from the bowl. (Dividing the dough in half results in two pretty generous pie crusts. If you desire a thinner crust, you may divide the dough into three crusts.)
Place in a large plastic bag (do not seal) and slightly flatten with a rolling pin. This makes it much easier to roll out the crust later. After flattening, seal the bag tightly.
Repeat with the other half of the dough and place the plastic bags in the freezer. I like to make several batches of pie crust at a time so I always have a crust ready to go.
For recipes other than this pot pie, remove from the bag and place on a lightly floured surface. With a rolling pin, begin rolling the dough from the center, outward. Be gentle and patient; it'll take a little time to get the dough completely rolled out.
If you think the bottom is really sticking to the surface below, use a nice, sharp spatula to loosen it and sprinkle some extra flour on top. Then flip it over to finish rolling. Remember to roll from the center in single, outward strokes; no back-and-forth rolling.
Again with a spatula, loosen and lift the pie crust and carefully lay it over a pie pan. Using your hand, lightly form the crust so that it fits inside the pan and overlaps the edges.
Because it's quick and easy, I just tuck the excess dough under itself above the rim. Then you can apply whatever decorative effects that you like to the edge. Or you can leave it plain if you'd like! Just tell yourself it's more rustic that way!
Fill the pie crust with filling and bake according to the pie recipe's directions. Or, for a pre-baked crust, fill with pie weights (or pinto beans placed on aluminum foil) and bake at 400 degrees F until golden, about 10 minutes.
Prepare the filling and pie crust ahead of time. Just keep them separate in the fridge until you're ready to assemble and bake. Or, fully assemble, cover tightly and freeze, unbaked, until ready.