Preheat oven to 400 degrees F.
Melt butter in a large saucepan over medium-high heat.
Add celery, carrots, onion and potatoes. Saute for 8-10 minutes, or until vegetables begin to soften.
Add garlic and season with salt and pepper.
Mix in flour, chicken broth and cream cheese. Let cook for 5 more minutes, stirring constantly.
Fold in chicken and peas.
Pour mixture into a baking sheet sprayed with nonstick cooking spray.
Roll out two puff pastry sheets to the width of the sheet pan, cut into 1-inch strips and lay over filling.
Use a sharp knife to cut off any excess dough hanging over the sides.
Whisk egg in a small bowl and brush over the top of the pot pie.
Cook for 30-35 minutes, or until the top is golden brown.
Remove from oven, garnish with fresh parsley and serve.