Preheat your oven to 400°F.
Melt butter in a saucepan over medium heat.
Add flour, and whisk until the roux forms smoothly.
Gradually add chicken broth, stirring continuously to avoid lumps.
Let it simmer until thickened.
Season with salt, pepper, and nutmeg for an extra kick!
In a mixing bowl, combine chicken, carrots, peas, onion, and celery.
Pour the sauce over, mixing well to coat everything evenly.
Transfer this filling into a pie dish, smoothing the top with a spoon.
Drape the puff pastry over, trimming the edges to fit.
Use a fork to seal the crust around the edge of the dish.
Brush the pastry with egg wash for a golden finish.
Make a few slits at the top to allow steam to escape.
Bake in the oven for 20 to 25 minutes, checking around the 20-minute mark.