Prepare either pie crust recipe through step 5, including chilling for at least 2 hours.

In a large pot, combine chicken, carrots, and celery. Add enough water to cover the chicken and vegetables, then place over medium-high heat. Bring to a boil, then allow to boil for 10 minutes. Remove from heat, drain, and set aside.

In a large skillet over medium heat, combine the butter, onions, and garlic. Stirring occasionally, cook until the onions are translucent and the butter is lightly browning. Whisk in the flour, salt, black pepper, thyme, chicken broth, and half-and-half. Cook and whisk until no flour lumps remain, then simmer over medium-low heat until thick.

Preheat oven to 425°F (218°C).

On a floured work surface, roll out one of the discs of chilled dough. Carefully place the dough into a 9-inch pie dish. Tuck the dough in with your fingers, making sure it is smooth. Trim the extra overhang of dough and discard.

Spoon the chicken and vegetable mixture into the crust. Scatter the frozen peas on top. Pour/spread the gravy evenly over top.

Roll out second half of pie crust dough and cover the pie with the second crust. Trim the extra overhang off the sides. Crimp the pie crust with a fork to seal the edges. Slice a few small slits in the top crust to allow steam to escape. Brush crust and edges with egg wash.

Bake for 32–38 minutes or until the top of the crust is golden brown. After 20 minutes of baking, cover the edges of the crust with aluminum foil to prevent the edges from getting too brown.

Remove from the oven and cool for at least 10 minutes before serving.