being an x-Philadelphian, chicken pot pie precedes McDonalds....
I've had the rottenest luck getting the consistency right, so I've come up with my own method:
whole chicken, cut up, poached with flavor - varies - celery seed, baby leaf, s&p, pepper flakes, diced onion, smashed garlic, <pick your favorites>
reserve the poaching liquid, make a thin roux, add chopped celery, chopped carrots, frozen peas. add cut up / chunkified poached chicken.
(I've been known to sneak in turnips, parsnips, leeks, green pepper, red pepper, onion....)
adjust sauce thickness - needs to be runnier than you thunk.
blind bake bottom crust (it's certainly required in Philadelphia....)
I use h/m pie crust, I use puff pastry, I use phyllo. heh, I'm easy to please.
after the blind bake, add the perfectly adjusted for consistency chicken yummies.
top with a round cut to size as a top crust; slit, egg wash if you gottum.
a sprinkle of ultra coarse sea salt ain't too bad.
bake to a nice color.