Preheat your oven to 400°F (200°C).
In a large skillet, combine the cream of chicken soup, chicken or turkey broth, and milk or heavy cream. Stir over medium heat until the mixture is well combined and heated through.
If you prefer a thicker sauce, mix the all-purpose flour with a small amount of water to create a slurry, then stir it into the sauce mixture. Cook for 2-3 minutes until thickened. It will continue to thicken as it bakes in the oven.
Stir in the leftover turkey, frozen mixed vegetables, garlic powder, onion powder, thyme, salt, and pepper. Cook for another 2-3 minutes, just until everything is heated and well combined. Remove from heat.
Unroll one of the pie crusts and place it into a 9-inch pie dish, pressing it gently into the bottom and sides. Pour the turkey mixture into the pie crust, spreading it out evenly.
Unroll the second pie crust and place it over the filling. Trim any excess crust, and crimp the edges together to seal. Cut a few small slits in the top crust to allow steam to escape.
Brush the top of the pie with a beaten egg for a golden finish.
Place the pie dish on a baking sheet to catch any drips and bake in the preheated oven for 40-45 minutes, or until the crust is golden brown and the filling is bubbly.
Check the Pie after 30 minutes. If the crust around the edges is browning too fast, cover the edges with foil and continue to bake.
Let the pot pie cool for 5-10 minutes before slicing and serving.