Preheat the Oven:
Preheat your oven to 375°F (190°C).
Prepare the Filling:
In a large skillet or saucepan, melt butter over medium heat. Add the onion, carrots, celery, and potatoes, cooking for 5–7 minutes until softened.
Sprinkle flour over the vegetables and stir to coat. Cook for 1–2 minutes to remove the raw flour taste.
Gradually whisk in chicken broth and cream, stirring constantly until the mixture thickens.
Stir in the chicken, peas, salt, pepper, thyme, and garlic powder. Remove from heat and let cool slightly.
Assemble the Pot Pie:
Roll out one sheet of pie crust and fit it into the bottom of a 9-inch pie dish. Trim any excess crust.
Pour the chicken and vegetable filling into the crust.
Roll out the second sheet of pie crust and place it over the filling. Seal the edges by pinching or crimping with a fork. Trim the excess crust and cut slits in the top to allow steam to escape.
Bake:
Brush the top crust with the beaten egg for a golden finish.
Place the pie dish on a baking sheet to catch any drips. Bake for 30–35 minutes or until the crust is golden brown and the filling is bubbly.
Cool and Serve:
Let the pie cool for 10–15 minutes before slicing and serving.