I usually par-bake my crust (because my wife likes the crust REALLY crispy). I go through a 3 step process.
I hand stretch out the dough in a 16" pan (My stone is not quite that big)
the crust is puffy and tapers down really thin (like a NY style thin crust).
I par-bake for about 7 minutes. Pull it out of the oven, put my sauce, toppings, etc. It goes back in the oven until the cheese has browned (I have to rotate it a couple of times). Pull it out of the oven again, slice it. And put the slices (usually 3-4 at a time) on the stone directly to get the crust nice and crispy). I put a little butter on the puffy part of the crust to give it some color. Every time I make this I NEVER have left overs.
NOTE: I never ever par-bake my crust ahead of time (which is what papa john's seems to be doing) my goes right back into the oven...