Preheat oven to 350 degrees F.
Melt butter in a large saucepan over medium-high heat.
Add carrots, celery, 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 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.
Cook Notes
You can use pie crust in place of the puff pastry, however, it does give a bit of a different texture and you will have to cook the dish an extra 10-15 minutes longer to make sure the dough is cooked through all the way.
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