Step 1

Preheat the oven to 400° and have ready a greased, 9" (preferably deep dish) pie tin.

Step 2

Add butter and oil to a large saucepan or Dutch oven over medium heat. As soon as the butter has melted, add the celery, carrots, and onion and sauté until softened, about 8 minutes. Add the garlic and sauté 1 minute more.

Step 3

Sprinkle flour over the vegetables and stir until evenly coated. Add the 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.

Step 4

Add the salt and 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 peas and the diced chicken, and set aside until ready to use.

Step 5

Roll out the pie dough so that it is a 1/4" 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.

Step 6

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.

Step 7

To make the egg wash, whisk together the egg and 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.

Step 8

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.

Step 9

Remove from the oven and allow to cool for 15-20 minutes before cutting into. Serve and enjoy.