1. Preheat oven to 425 degrees.
2. In a large saucepan, combine chicken and celery. Add enough water to cover the chicken and boil for about 12-15 minutes, until cooked, then drain and set chicken and celery aside. (See note below for using rotisserie chicken)
3. Melt the butter in the saucepan over medium heat.
4. Add the onion and cook for about 2 minutes, stirring regularly, until tender and translucent.
5. Stir in the flour, thyme, salt and pepper until combined.
6. Slowly add the chicken broth and cream and stir until well combined and no longer lumpy.
7. Simmer the mixture over medium low heat until thickened, about 15 minutes or so. You want it to be like a very thick gravy. The thicker it is, the thicker it’ll be in your pot pie.
8. Add the chicken, celery, peas and carrots and stir to combine. Set aside.
9. Roll out one of the prepared pie crust into a 9 inch pie plate.
10. Add the filling to the pie crust, then cover with the second pie crust and crimp the edges.
11. Brush the top of the pie with the beaten egg.
12. Bake for about 20 minutes, then add a pie crust ring to keep it from over browning and continue cooking for an additional 10-20 minutes. Remove from the oven and serve. Keep in mind that as the pot pie cools, the sauce thickens further.