Preheat oven to 425 degrees.
Shred chicken into bite sized pieces. Measure out about 3 cups or more for the pot pie.
Melt butter in a medium stock pot. Add celery, onion, potato and carrots then cook until tender.
Add flour and stir until well mixed. Cook at least one minute.
Stir in half and half, chicken broth, and seasonings - and heat to a simmer, stirring constantly. Cook until thickened, approximately 6-7 minutes.
Remove from heat, and add chicken and frozen vegetables to pot. Combine well.
Pour into prepared pie pan and top with second crust. Seal together with your fingers, careful to crimp the edges.
Using a sharp knife, cut a few slits on top crust to allow steam to escape during baking process.
Brush beaten egg on top crust.
Bake on 425 degrees for 40 to 45 minutes, or until the top is nice and golden brown. Bake 20 minutes uncovered then cover the edges of the crust for the remaining time. Bake on lower rack of the oven.
