Preheat your oven to 425°F (220°C).
In a large skillet, heat a drizzle of oil over medium heat and add the diced onion and celery. Sauté until tender, about 5 minutes.
Add the shredded turkey and frozen vegetables to the skillet, followed by the cream of chicken soup and milk. Season with garlic powder, thyme, salt, and pepper, stirring until well combined and heated through, roughly 5 minutes.
Lay one pie crust into a 9-inch pie dish, ensuring it fits snugly.
Spoon the turkey and vegetable mixture into the crust, spreading it evenly.
Unroll the second pie crust and place it on top of the filling. Press the edges together to seal, crimping with a fork or fingers.
Make several small slits in the top crust to allow steam to escape.
Brush the top with the beaten egg for a golden crust.
Bake in the oven for 30-35 minutes, or until the crust is golden brown. Cover edges with aluminum foil if they brown too quickly.
Allow the pie to cool for about 10 minutes before slicing and serving.