01 - Preheat the oven to 400°F.
02 - Melt butter in a large saucepan over medium heat. Add onion, carrots, celery, and potatoes; cook for 6 to 8 minutes until vegetables start to soften.
03 - Stir in flour and cook, stirring constantly, for 1 minute to form a roux.
04 - Gradually whisk in chicken broth and milk. Season with salt, black pepper, thyme, and garlic powder. Simmer, stirring frequently, until sauce thickens, approximately 5 minutes.
05 - Remove from heat and fold in cooked chicken and peas.
06 - Transfer the filling to a 9-inch pie dish. Roll out pie dough to cover filling, trim edges, seal, and cut 2 to 3 vents on top. Brush with beaten egg if desired.
07 - Bake in the preheated oven for 30 to 35 minutes until the crust is golden brown.
08 - Allow the pot pie to rest for 10 minutes before serving.