1. 1. Prepare Your Baking Dish and Oven: Preheat your oven to 400 F (200 C). Lightly grease a 9-inch pie dish or a similar-sized baking dish. Unroll your thawed pie crust and set it aside.

2. 2. Saute Aromatics: In a large skillet or Dutch oven, heat the olive oil or butter over medium heat. Add the chopped yellow onion and cook for 3-4 minutes until softened and translucent. Stir in the minced garlic and cook for another minute until fragrant.

3. 3. Create the Roux: Sprinkle the all-purpose flour over the cooked onions and garlic. Stir constantly for 1-2 minutes, allowing the flour to cook slightly and form a paste (this is called a roux). This will thicken your pot pie filling.

4. 4. Whisk in Liquids and Seasonings: Gradually whisk in the chicken or turkey broth, followed by the milk. Continue whisking until the mixture is smooth and starts to thicken. Stir in the dried thyme, dried rosemary, salt, and black pepper. Bring the mixture to a gentle simmer, stirring occasionally, until it thickens to a gravy-like consistency.

5. 5. Combine Filling Ingredients: Remove the skillet from the heat. Stir in the cooked turkey and frozen mixed vegetables. Mix everything well to ensure the turkey and vegetables are evenly coated with the creamy sauce. Pour the entire filling mixture into your prepared pie dish.

6. 6. Top with Pie Crust and Bake: Carefully place the thawed pie crust over the filling in the pie dish. Crimp the edges of the crust to seal it to the dish. If desired, cut a few small slits in the top of the crust to allow steam to escape. For a golden-brown finish, brush the top of the crust with the beaten egg (egg wash).

7. 7. Bake Until Golden and Bubbly: Bake for 25-30 minutes, or until the crust is golden brown and the filling is bubbly. If the crust starts to brown too quickly, you can loosely tent it with aluminum foil.

8. 8. Cool and Serve: Let the pot pie cool for 5-10 minutes before slicing and serving. This allows the filling to set slightly and makes for easier serving.