Prepare either pie crust recipe through step 5, including chilling the dough for at least 2 hours. (I often make the crust the night before.) You'll be using both crusts for this recipe.

In a large pot, combine the cubed chicken, sliced carrots, and celery. Add enough water to cover the chicken and vegetables. Place over medium-high heat and bring to a boil. Boil for 10 minutes, then remove from heat, drain, and set aside.

In a large skillet over medium heat, melt the butter. Add the chopped onions and minced garlic. Stir occasionally 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 lumps remain, then simmer over medium-low heat until thickened, about 10 minutes. It should be a thick gravy; simmer longer if needed. Taste and adjust seasonings, adding more thyme if desired. Remove from heat and set aside.

Preheat your oven to 425°F (218°C).

On a floured work surface, roll out one of the discs of chilled dough until it’s about 12 inches in diameter. Carefully place the dough into a 9-inch pie dish that’s 1.5–2 inches deep. Tuck the dough in with your fingers and trim any excess overhang.

Spoon the chicken and vegetable mixture into the bottom crust. Scatter the frozen peas on top and pour the gravy evenly over everything.

Roll out the second disc of dough as you did the first. Cover the pie with the second crust and trim any excess overhang. Crimp the edges with a fork to seal. Slice a few small slits in the top crust to allow steam to escape, then brush the crust and edges with the egg wash.

Bake for 32–38 minutes, or until the top crust is golden brown. After 20 minutes, cover the edges of the crust with aluminum foil or use a pie crust shield to prevent over-browning.