1. Prepare the pie crust dough according to your recipe instructions and chill for at least 2 hours before using.

2. In a large pot, add the chicken, carrots, and celery. Cover with water and bring to a boil over medium-high heat. Cook for about 10 minutes until the chicken is cooked through and the vegetables begin to soften. Drain and set aside.

3. In a large skillet over medium heat, melt the butter. Add the chopped onion and garlic, cooking until softened and fragrant.

4. Stir in the flour, salt, pepper, and dried thyme. Slowly whisk in the chicken broth and half-and-half until smooth.

5. Simmer the mixture over medium-low heat for about 10 minutes, stirring often, until thick and creamy.

6. Preheat the oven to 425°F.

7. Roll out one pie crust on a lightly floured surface into a 12-inch circle. Place it into a deep 9-inch pie dish and trim any excess dough.

8. Spread the chicken and vegetable mixture into the crust. Sprinkle the frozen peas evenly on top, then pour the thick gravy over everything.

9. Roll out the second crust and place it over the filling. Trim excess dough and crimp the edges to seal. Cut a few small slits in the top crust for ventilation.

10. Beat the egg with 1 tablespoon milk and brush over the crust.

11. Bake for 32–38 minutes, or until the crust is golden brown. If the edges brown too quickly, cover them loosely with foil halfway through baking.

12. Let the pot pie cool for at least 10 minutes before serving.