Preheat oven to 375°F (190°C). Roll out the pie crust and line a 9-inch pie dish. Trim excess edges and set aside.

In a large skillet, melt butter over medium heat. Add onions, celery, and carrots. Sauté for 5 minutes until softened.

Sprinkle flour over the vegetables and stir well to coat. Cook for 1-2 minutes to remove the raw flour taste.

Gradually whisk in the chicken broth and heavy cream. Bring to a simmer, stirring constantly until the mixture thickens.

Add the cooked turkey, frozen mixed vegetables, thyme, parsley, salt, and pepper. Stir well and cook for another 2-3 minutes.

Pour the turkey mixture into the prepared pie crust. Cover with the second pie crust or create a lattice top. Seal the edges and cut slits on top for ventilation.

Brush the top crust with beaten egg for a golden finish. Bake for 35-40 minutes or until the crust is golden brown and the filling is bubbly.

Let the pot pie cool for 10 minutes before serving to allow the filling to set.