In a large skillet, melt the butter over medium heat. Add the diced onion, carrots, and celery, and cook until the onion is translucent, about 5 minutes.
Stir in the diced chicken and cook until no longer pink, about 7-8 minutes.
Sprinkle the flour over the chicken and vegetable mixture, stirring well to coat. Cook for 1-2 minutes to eliminate the raw flour taste.
Gradually pour in the chicken broth and whole milk while stirring, bringing the mixture to a simmer. It will thicken as it cooks.
Add the peas, diced potatoes, thyme, garlic powder, salt, and pepper. Stir well and simmer for another 5 minutes until the mixture is heated through. Remove from heat.
Roll out one pie crust and place it in a 9-inch pie dish. Spoon the chicken filling into the crust, making sure it's evenly distributed.
Roll out the second crust and place it over the filling. Crimp the edges to seal the pie and cut several slits in the top for steam to escape.
Brush the top crust with the beaten egg for a golden finish.
Bake in the preheated oven for 30-35 minutes or until the crust is golden brown and the filling is bubbly.
Allow to cool for 10 minutes before slicing and serving.
Notes
Serve the pot pie warm in shallow bowls, garnished with fresh chopped parsley for a pop of color.