Make the dough: cut the 225 grams cold unsalted butter in ½ inch cubes and freeze them while you measure and mix the dry ingredients
in a food processor: combine the 255 grams all-purpose flour, 1 teaspoon sugar, and 1 teaspoon salt and pulse three or four times to mix. Retrieve the butter cubes from the freezer, scatter over the dry mixture, and pulse until pea-sized clumps form. Add the 3-5 tablespoons ice water, 1tbsp at a time, and pulse to mix, adding just enough water for the dough to come together.
turn the dough out onto a clean floured surface, gather in a mound, and knead a few times to smooth out. divide in half, and gently pat and press into a circle about 1 inch thick. Wrap in plastic and refrigerate for at least 2 hours or up to three days.
Preheat the oven to 400° and have ready a greased, 9" (preferably deep dish) pie tin.
Make the pie filling: Add 2 tablespoons butter and 1 tablespoon canola oil to a large saucepan or Dutch oven over medium heat. As soon as the butter has melted, add the 2 stalks of diced celery, 2 diced carrots, and diced yellow onion and sauté until softened, about 8 minutes. Add the 1 clove of minced garlic and sauté 1 minute more.
Sprinkle the ⅓ cup + 1 tablespoon flour over the vegetables and stir until evenly coated. Add the 3 cups chicken broth a splash at a time, whisking after each addition, until the mixture begins to resemble a thick pudding. Once this consistency is reached, the remaining broth can be added in.
Add the 1 teaspoon salt and ½ teaspoon pepper and increase the heat to medium-high. Allow the mixture to simmer, stirring often, about 5 minutes or until slightly thickened. Stir in the ½ cup frozen peas and the 2 cups diced chicken and set aside until ready to use.
Roll out the pie dough so that it is a ¼" thick. Lay one dough round on across the bottom of the pie dish and allow the excess to lay over the sides of the dish.
Pour the chicken and vegetable filling into the dish. Roll out the second dough round just the same and place it over the dish. Crimp the edges of the pie crust together.
To make the egg wash, whisk together the 1 large egg and 1 tablespoon water, and using a pastry brush, lightly brush the mixture across the top crust and the edges. Create vent holes in the center of the pie, and transfer to a sturdy, rimmed baking sheet to catch any spillage.
Bake the pie for 20 minutes. Then, reduce the temperature to 350°, and bake for 25-28 minutes more, or until the top is golden-brown. Use a pie shield to prevent the edges from over-browning.
Remove from the oven and allow to cool for 15-20 minutes before cutting into. Serve and enjoy.
