Mix all dry ingredients and the butter together until very well incorporated.
Make a well in the center of the mixture.
Add 3 T of the cold water and mix well with a pastry blade.
Add 2 T of the cold water and mix well with a pastry blade.
Shape the dough into a ball and check the consistency. The dough should stick together, but should still be dry and flaky.
If necessary, add an additional tablespoon of cold water and mix well.
Wrap the dough tightly in plastic wrap and chill for a minimum of a few hours, preferably overnight.
CHICKEN POT PIE
Season the chicken with salt and pepper and reserve.
Add the chicken broth to a medium pot over high heat. Bring to a boil.
Add the chicken pieces to the boiling stock, reduce heat and simmer for 1 minute. Turn off the heat and let the chicken rest until it is just cooked through, about 2-4 minutes longer, depending on the size of the pieces. Spread the cooked chicken on a sheet pan to cool.
Add one tablespoon of butter to a large pot over medium heat. Once the butter has melted, add the mirepoix (mixture of diced onion, carrot, and celery). Add a dash of salt, stir, and sweat (slowly cook without browning) the mirepoix until the vegetables are tender.
Drain the diced potatoes and add to the pot. Season and stir to combine. Sweat briefly.
Ladle enough of the broth used to cook the chicken to just cover the mirepoix. Simmer until the potato is tender.
Meanwhile, prepare a roux. Melt 2 tablespoons butter in a small skillet over medium heat. Once melted, slowly whisk in 2 tablespoons flour, whisking after each addition until fully incorporated. Cook the roux briefly, whisking continuously, until the butter and flour is completely combined and the roux is smooth. Reserve off heat.
Bring the remaining stock used to cook the chicken back to a boil.
Slowly add the prepared roux to the boiling stock, whisking to incorporate it into the broth. Repeat this process until all of the roux has been added. Simmer the broth for a minimum of 5 minutes to cook out the flour, stirring occasionally, until the sauce is thickened. Slowly stir in the heavy cream, whisking to combine (Sauce Supreme).
When the potatoes in the other pot are tender, add the peas to the mirepoix and continue to simmer for 4-6 minutes.
Stir in the reserved Sauce Supreme. Bring the mixture back to a boil briefly and reduce to the desired consistency.
Remove the mixture from the heat and empty it into a large mixing bowl over a bowl of ice water (ice bath). Cool completely, add the reserved cooked chicken and chopped parsley, and stir to combine all ingredients.
Preheat the oven to 375 F. Roll the pâte brisée (see accompanying recipe) very thin (about 1/8″) and to a shape that is just larger than the casserole dish that you will be using to bake off the final dish.
Liberally grease the top rim of the casserole dish with the remaining butter. Empty the cooled filling into the dish. The rolled pâte brisée crust will be flaky and fragile. Use a pastry blade or wide spatula to carefully transfer it from the work surface to the top of the casserole dish. If the crust tears, simply piece it back together with your fingers and/or use a smaller piece of crust to cover any gaps, tears or holes. When you are satisfied with the placement of the crust, brush the entire surface with egg wash (to promote browning during baking).
Transfer the casserole dish to the preheated oven. Bake for approximately 30 minutes, or until the crust is golden brown and the filling is hot and bubbly. Serve immediately.