Preheat your oven to 425°F (220°C).

In a large skillet, melt the butter over medium heat. Add the chopped onion and celery, and sauté until they are tender, about 5 minutes.

Stir in the flour until well combined, and cook for 1-2 minutes to get rid of the raw flour taste.

Gradually whisk in the chicken broth and milk, bringing the mixture to a simmer. Cook until the sauce is thickened, about 5-7 minutes.

Stir in the leftover turkey, frozen peas and carrots, frozen corn, salt, pepper, thyme, and rosemary. Cook until everything is heated through, about 3-5 minutes. Remove from heat.

Roll out the pie crust on a lightly floured surface if needed. Fit the pie crust into a 9-inch pie dish.

Pour the turkey and vegetable filling into the pie crust.

Roll out the second pie crust (if using a double crust) and place it over the filling. Trim any excess dough and crimp the edges to seal.

Cut a few small slits in the top crust to allow steam to escape. Brush the top with the beaten egg to give it a golden color.

Place the pie on a baking sheet to catch any drips. Bake in the preheated oven for 30-35 minutes, or until the crust is golden brown and the filling is bubbly.

Let the pot pie cool for about 10 minutes before serving. This will help the filling set and make it easier to slice.