01 - Preheat the oven to 400°F.
02 - In a large skillet, melt the butter over medium heat. Add the onion and celery, sautéing for 3 to 4 minutes until softened and translucent.
03 - Sprinkle the flour over the softened vegetables and cook, stirring constantly, for 1 to 2 minutes to form a smooth roux.
04 - Gradually whisk in the chicken broth and whole milk. Continue cooking and stirring until the sauce thickens, approximately 5 minutes.
05 - Fold in the diced potatoes, frozen carrots, frozen peas, diced chicken, salt, black pepper, dried thyme, and dried parsley. Simmer for 8 to 10 minutes until the vegetables are just tender.
06 - Pour the filling into a 9-inch pie dish or deep baking dish, spreading it evenly.
07 - Roll out the puff pastry and drape it over the filling. Trim any excess dough, press the edges firmly to seal, and cut a few slits in the top to allow steam to escape during baking.
08 - Brush the pastry crust evenly with the beaten egg to promote a golden, glossy finish.
09 - Bake for 35 to 40 minutes until the crust is deep golden brown and the filling is bubbling at the edges.
10 - Allow the pot pie to cool for 10 minutes before slicing and serving.