- 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.