If you'd like to make something with cauliflower and/or broccoli, try this: trim and wash the florets (keep the stems for something else if you like). Blanch them in boiling salted water for 3 or 4 minutes (a little longer maybe for cauliflower). Drain them and dump them into some cold water, then drain them.
Now (or before now): get a heavy roasting pan (like a big earthenware or cast iron lasagna pan, or something like that - the heavier the better) hot in a 375 degree (F) oven. That should take about 15 or 20 minutes - we want it hot. Pull it out of the oven carefully, and then add some oil. Spread the oil around with a silicone brush or by tilting the pan (carefully please; don't burn yourself and sue me) and then add the drained broccoli/cauliflower. Sort-of toss those around (if you've got some spray olive oil, you can squirt them with that) and then add kosher/sea salt and black pepper.
Roast those in the oven for about 20 minutes, possibly tossing them around halfway through.
Now what you've got is the best tasting cauliflower/broccoli in the world. You can add those roasted florettes to a quiche or to a pot pie or to anything like that. I add thusly roasted cauliflower to Indian "dal" preparations and it's awesome.
Here's another tip: if you want to add cubed potatoes but you don't want them to turn to mush, try this. Cube the raw potatoes. Get some water warming on the stove, but when it's still just warm (less than 130 degrees F) add the potatoes. Keep the fire on, but monitor the temperature very carefully. When the water gets up to 138 degrees F, drop the fire a lot and try to keep it at that temperature for about 10 minutes. After that, raise the fire and let the potatoes boil as you normally would.
That trick will allow a natural enzyme in the potatoes to "firm up" the starch, and they'll end up cooked but not mushy. You can then add them to your pot pie with the confidence that they'll more-or-less hold together. (Beets do this kind-of automatically; it's really hard to cook a beet until it's mush.)
I'd avoid the whole reheating issue altogether and simply keep the uncooked pie in the fridge, covered in plastic wrap, then bake it as normal when ready. The only issue you might have is if your filling is very runny, in which case you could par-bake it a little before filling to help it 'seal'.
Best Answer
As far as I can see, you don't defrost the pie before baking in the recipe so some of the time in the oven would just be defrosting the pie; so this could be done in advance by bringing it out of the freezer an hour and a half before baking say. As the chicken is already cooked it looks like all you're doing is cooking the pastry so you could just use thinner pastry which would cook quicker, or better you could use layers of phyllo pasty which would cook a lot quicker but of course wouldn't puff up like the puff pastry.
If you follow this it could probably bake for just 25 minutes or there about.
Hope this helps!