Preheat oven to 350 degrees F.
Melt butter in a large saucepan over medium-high heat. Add carrots, celery, onion, and potatoes. Sauté 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 12-inch oven safe skillet.
Roll out a sheet of puff pastry and place on top of skillet. 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 18-20 minutes, or until the top is golden brown.