Preheat the oven to 400°F/200°C.
Prepare the ingredients: Chop the turkey and set it aside. Finely chop the onion, carrot, and celery. Place the peas on the counter to let them defrost slightly until you need them.
Make the gravy: Melt the butter in a large skillet. Cook the vegetables with a pinch of salt on medium-low heat for about 5 minutes until softened. Sprinkle the flour on top and stir continuously for about 2 minutes until the flour is golden and loses its rawness. Don’t let it get dark. Gradually add the chicken stock and then the milk. Whisk constantly to avoid any lumps. Reduce slightly for about 5 minutes, often stirring.
Add the chopped meat, peas, and parsley and stir well to combine. Adjust the taste with salt, pepper, and nutmeg. Transfer the mixture to the pie dish.
Place the puff pastry inside the dish on top of the filling and tuck the pastry around the edges. Trim the edges if too much pastry is hanging over, and fold the rest around the edges. Make 2-3 slits on top to allow the hot air to escape.
Mix the egg and 1 tablespoon of milk in a small bowl. Brush the pastry with the egg wash.
Bake turkey pot pie for 35-40 minutes until the mixture is bubbly and the pastry is golden.