01 - Preheat the oven to 400°F (200°C).
02 - Melt butter in a large skillet over medium heat. Add onion, carrots, and celery, sautéing until softened, approximately 5 minutes.
03 - Stir in flour and cook for 1 minute, stirring constantly to form a roux.
04 - Gradually whisk in chicken broth and whole milk. Cook, stirring continuously, until sauce thickens, about 3 to 5 minutes.
05 - Add cooked chicken, peas, salt, black pepper, dried thyme, and garlic powder. Stir thoroughly and remove from heat.
06 - Fit one pie crust into a 9-inch pie dish and evenly spread the chicken filling inside.
07 - Cover with the second pie crust. Trim excess dough, crimp edges to seal, and cut small slits in the crust to vent steam.
08 - Brush the top crust with beaten egg to ensure a golden, glossy finish.
09 - Bake in the preheated oven for 35 to 40 minutes until crust is golden brown and filling is bubbling.
10 - Allow the pie to cool for 10 minutes before slicing and serving.