01 - Set the oven temperature to 400°F.
02 - Melt butter in a large skillet over medium heat. Add diced onions, carrots, celery, and potatoes; cook for 8 to 10 minutes until tender.
03 - Sprinkle flour into the skillet, stirring constantly and cooking for 1 to 2 minutes to form a roux.
04 - Gradually whisk in the broth followed by milk, stirring continuously until the mixture thickens, about 4 to 5 minutes.
05 - Mix in salt, pepper, thyme, and sage. Add turkey and peas, then simmer for 2 to 3 minutes before removing from heat.
06 - Pour the prepared filling into a 9-inch pie dish or comparable baking dish.
07 - Cover the filling with the thawed puff pastry sheet, trim excess, seal edges firmly, and cut small slits on top to release steam.
08 - Brush the pastry surface evenly with the beaten egg to achieve a golden crust.
09 - Place the assembled dish in the oven and bake for 30 to 35 minutes until the crust is golden and the filling bubbles.
10 - Allow the dish to stand for 10 minutes to set before slicing and serving.