01 - Preheat the oven to 400°F (200°C).
02 - Melt butter in a large skillet over medium heat; add onion, carrots, and celery, and sauté until softened, about 5 minutes.
03 - Stir in flour and cook, stirring constantly, for 1 minute to form a roux.
04 - Gradually whisk in chicken broth and milk; cook while stirring until the mixture thickens, approximately 3 to 5 minutes.
05 - Add cooked chicken, peas, salt, black pepper, thyme, and garlic powder; mix well and remove from heat.
06 - Place one pie crust into a 9-inch pie dish; pour the filling evenly into the crust.
07 - Place second pie crust on top; trim and crimp edges to seal. Cut several slits in the top crust to allow steam to escape.
08 - Brush the top crust with beaten egg to achieve a golden finish.
09 - Bake for 35 to 40 minutes until the crust is golden brown and the filling is bubbling.
10 - Let the pie cool for 10 minutes before slicing and serving.