Preheat the oven according to the instructions on the biscuit package. Spray the cavities of a 12-cup muffin pan with cooking spray.
Mix together the chicken, cream cheese, dressing, wing sauce, shredded cheese, carrots and celery in a large bowl.
Lightly beat the egg with 1 tablespoon water in a small bowl to form an egg wash.
Using a piece of string, cut each biscuit in half so that you have 2 thin rounds. Flatten the rounds and press 12 of them into the prepared muffin pan.
Evenly divide the chicken filling among the muffin cups and top with the remaining 12 biscuit rounds. Try to press the edges together and seal with the bottom portion of dough if possible. Cut 2 small slits in the top to allow steam to escape.
Brush the tops of each pot pie with the egg wash. This will help them turn a nice golden brown. Bake in the oven until the dough is cooked through and golden brown, about 20 minutes.