Preheat your oven to 425°F (220°C).

In a large skillet, heat the olive oil or butter over medium heat. Add the frozen mixed vegetables and sauté for about 5 minutes until they are tender.

Sprinkle the flour over the vegetables and stir to combine, cooking for another minute to eliminate the raw flour taste.

Gradually whisk in the turkey or chicken broth and milk, ensuring there are no lumps. Continue to cook, stirring frequently, until the mixture thickens, about 5-7 minutes.

Add the shredded or diced turkey, garlic powder, onion powder, dried thyme, salt, and pepper. Stir everything together until well combined. Remove from heat.

Roll out the pie crust and fit it into a 9-inch pie dish. Pour the turkey and vegetable mixture into the crust.

If using a second pie crust, place it over the filling, crimping the edges to seal. If you prefer a single crust, simply leave the top open. Cut a few slits in the top to allow steam to escape.

Brush the top crust (or edges) with the beaten egg for a golden finish.

Bake in the preheated oven for 25-30 minutes, or until the crust is golden brown and the filling is bubbly.

Remove from the oven and let it cool for about 10 minutes before serving.