01 - Preheat the oven to 400°F.
02 - Melt butter in a large skillet over medium heat. Add onions, carrots, celery, and potatoes; sauté for 8 to 10 minutes until softened.
03 - Stir in flour and cook for 1 to 2 minutes, stirring constantly.
04 - Gradually whisk in broth and milk, cooking and stirring until the mixture thickens, about 4 to 5 minutes.
05 - Add salt, pepper, thyme, and sage. Stir in turkey and peas, then simmer for 2 to 3 minutes. Remove from heat.
06 - Pour the filling into a 9-inch pie dish or equivalent baking dish.
07 - Drape thawed puff pastry over the filling, trim excess, seal edges, and cut small slits on top to allow steam to escape.
08 - Brush the pastry surface with beaten egg for a golden finish.
09 - Bake for 30 to 35 minutes until the crust is golden and the filling bubbles.
10 - Let stand for 10 minutes before slicing and serving.