01 - Preheat oven to 400°F. Lightly grease a 9x13-inch baking dish.
02 - Melt butter in a large skillet over medium heat. Add onion, carrots, and celery; cook for 5 to 6 minutes until softened.
03 - Add flour to the skillet and stir constantly for 1 minute to form a roux.
04 - Gradually whisk in chicken broth and milk. Stir in salt, pepper, thyme, and garlic powder. Simmer for 3 to 4 minutes until thickened.
05 - Remove from heat and fold in shredded chicken and peas until evenly combined.
06 - Transfer filling into the prepared baking dish, spreading evenly.
07 - Unroll pie dough and place over filling. Trim excess dough and cut slits in the crust to vent.
08 - Brush the crust surface with beaten egg for a golden finish.
09 - Bake for 35 to 40 minutes until crust is golden brown and filling bubbles.
10 - Allow to rest for 10 minutes to set before serving.