A word about the ingredients. I like to use boneless, skinless chicken breast boiled then shredded. You can successfully use canned chicken but it will give you an entirely different texture. Similarly, if you shred the chicken these pies come out differently than if you cube it. Your choice!
In a medium saucepan combine stock, carrots, celery, chicken, and peas. Bring to a boil.
Mix cornstarch with milk; stir into stock mixture. Cook 5 minutes while stirring. Remove from heat and let cool for 1 hour.
Preheat oven to 325 degrees F (175 degrees C).
Stir cheese into filling mixture and pour into 9 inch pie crust. Do not overfill.
Top with second crust, seal edges and cut slits in top crust.
Bake on a cookie sheet for 35 to 40 minutes or until crust is golden brown. Watch the edges of the crust, in my oven they tend to burn and I must cover them with foil (or "pie crust protectors" if you have them).