Bake chicken breast at 350 degrees for approximately 45 minutes or till juices run clear,Set aside and let cool. Cut into pieces once cooled. Set out pie crust to let come to room temperature.
Cook carrots with a chicken bouillon till tender, drain well, cook potatoes till fork tender,drain well. Mix carrots and potatoes together,prepare stuffing according to directions on the box, and add stuffing to the mixture.
Put pie crust in glass pie dish. Layer carrot, potatoes,stuffing mixture, then chicken, pour some gravy to moisten. Keep repeating, mixture, chicken, a bit of gravy. It will be quite high and full. Top with crust and brush with beaten egg. Bake at 425 for ten minutes watching for browning. Turn heat back to 350 bake about another 45 minutes or till top is brown and flaky. Let stand for ten minutes. Remember to cover edges with foil so they do not over brown.
I recommend putting this on a cookie sheet and foil under the pot pie. This makes covering the edges easier. The cookie sheet will catch spills too. This pot pie is not like a traditional pie with everything swimming in gravy. It is more firm inside.