01 - Preheat the oven to 400°F.
02 - Melt the butter in a large skillet over medium heat. Add onions, carrots, and celery; cook until softened, about 5 to 6 minutes.
03 - Sprinkle flour over the vegetables and stir constantly for 1 minute to cook the flour.
04 - Gradually whisk in chicken broth and milk. Continue cooking until the mixture thickens and bubbles, approximately 3 to 4 minutes.
05 - Stir in cooked chicken, peas, salt, black pepper, thyme, and garlic powder until well combined. Remove from heat.
06 - Transfer the filling into a 9-inch pie dish.
07 - Roll out the pie dough and cover the filling. Trim excess dough, crimp edges to seal, and cut small slits on top for steam release.
08 - Brush the crust with the beaten egg to promote browning.
09 - Bake for 35 to 40 minutes until the crust is golden brown and the filling bubbles.
10 - Allow the pot pie to rest for 10 minutes before serving.