Chicken pot pie: synonymous with love for many, or just eating your feelings. It is iconic. Read this entire recipe from start to finish. You need to understand what you are getting into.
These pies are not difficult, but it is imperative to accomplish more than one thing at a time. For this recipe, you must cook the chicken before it goes in the pie. You also cook the vegetables and make the gravy. Organize your tasks well and you can accomplish these things at the same time.
The best pot for this is a Dutch oven or a big, somewhat deep cast-iron one.
Heat the olive oil in a stockpot over medium-high heat and add the onion when hot. Stir, and when it becomes fragrant, add the celery and carrots. Sauté for a few minutes. Season the chicken with salt inside and out and put in a stockpot.
Cover with cold water and add the stems from 1 bunch parsley, thyme, and peppercorns. The stock will begin to bubble after about 25 minutes. As this happens, a dirty foam will collect on the surface of the liquid. Get a ladle and discard it. You are now skimming the scum. Skim it all before it comes to a boil and reincorporates into the stock. Cover the pot immediately with a lid and turn the burner off.
After 30 minutes, check the chicken. Pull on the drumstick with tongs; it should be very wiggly. Pull out the chicken and let it cool until you can pick it. Take out the skin and bones, put back in the stockpot, and let it simmer for 1 more hour.
Shred the chicken into good pieces, not too chunky and nothing like cat food. Strain the stock and reserve 2 cups for gravy. Stock freezes really well or keeps in the refrigerator for up to 4 days.
Place a cast-iron pan over medium heat and put in the fat. As it melts, whisk the flour in batches so it can be incorporated into the fat as you go. (This helps cut down on the whisking lumps out on the back end.)
Keep whisking the roux as it is mixed. If it bubbles a bit too much, reduce the heat. (A roux is a thick entity that can burn easily.) Keep whisking the roux. Reduce the heat to low. (Even though the flour is mixed in with the fat, it is still separate, so the roux has to keep on cooking to get the flour flavor out.) The entire cooking time for this roux is about 10 minutes.
Add the stock to the roux. (Always add in a slow, steady stream to a roux while whisking; it cuts down on clumping and ensures that the liquid is absorbed.) Next, add the white wine and heavy cream in the same manner.
Whisk everything together and let it set for a bit, whisking every now and again. Increase the heat to medium or even a bit higher if you are attending to it. It needs to reduce, and the disparate flavors need to cook together. If you can still taste the separate components of a sauce then it is still raw and needs to cook longer. This gravy takes about 25 minutes to cook.
To find the sweet spot between too runny and too thick: Take your spatula or spoon out of the gravy and swipe your finger across it. The line you create should keep its shape and the sauce should be a delicate balance between translucent and opaque. (Since it will cook and reduce a bit more in the pie, it is better to err on the side of a little thin rather than really thick.) Season with salt and pepper, to taste.
Combine the ingredients together in a bowl thoroughly and set aside.
Heat the fat in a Dutch oven over medium heat. Add the onions and sauté them until translucent, about 10 minutes. Once they are soft and fragrant, add the celery, carrots, and peas. Mix together.
Continue cooking until they are just soft. Add the 3 cups of the shredded chicken, mix together, and then add the gravy. Mix it all together and season with salt and pepper, to taste. Let cool before putting into the pie crust.
Preheat the oven to 425 degrees.
Roll out the chilled bottom crust to 1/8-inch thickness. It should be about 13 inches in diameter. Place in a pie plate or cast-iron pan. Trim the edges with kitchen shears so that there is no more than ¼ inch of overhang. Lift and crimp the overhang along the rim of the pie pan. Chill the bottom crust in the refrigerator or freezer.
Chop up the parsley leaves and mix it into the chilled filling. Pull out the chilled top crust from the refrigerator and roll out in the same manner and thickness.
Get the pie plate or cast-iron pan out of the refrigerator. If using a pie bird, place it, beak up, in the middle of the bottom crust and spoon the filling around it. If not using a pie bird, put the filling in the crust. Place the filled pie pan adjacent to the top crust and treat it the same way, quickly flip the top crust in half, and place on top of the pie.
Unfold the other half of the top crust over the pie. If there is a pie bird, just punch its beak through the top crust to vent. Lift the edges of the top crust up so the crust sits on top of the filling, not just stretched across it.
Trim the edges to be flush with the bottom crust and crimp them together. Cut slits in the top crust even if you do use a pie bird. Brush the top crust with the wash, and season it with sea salt, to taste. Put in the preheated oven and bake until golden brown, about 45 minutes.