01 - Set oven temperature to 400°F (200°C).
02 - In a large skillet, melt butter over medium heat. Add onion, carrots, and celery, cooking until softened, approximately 5 minutes.
03 - Stir in flour and cook constantly for 1 minute to remove raw taste.
04 - Gradually whisk in chicken broth and milk, cooking and stirring until the mixture thickens, about 3 to 5 minutes.
05 - Add cooked chicken, peas, salt, black pepper, thyme, and garlic powder. Mix thoroughly and remove from heat.
06 - Place one pie crust into a 9-inch pie dish, fitting it evenly.
07 - Pour the chicken mixture into the prepared crust, spreading evenly.
08 - Place the second pie crust on top, trim excess dough, crimp edges to seal, and cut small vents in the top crust for steam release.
09 - Brush the surface of the top crust with the beaten egg to enhance browning.
10 - Bake in the preheated oven for 35 to 40 minutes until the crust is golden and the filling bubbles.
11 - Allow the dish to rest for 10 minutes before slicing and serving.