Puffy Pizza Dough
Are you channeling your best self with this comment? (If you're not sure, check out our Code of Conduct.)
HalfPint is a trusted home cook.
How hot was the oven? A screaming hot oven (~500F) can really make a difference in rise. It often provides 'oven spring' to bread.
I'm not familiar with the recipe you mention, but pizza dough is just bread. In order to puff, as with rustic style breads, you want a moist dough with a loose structure; it should be kneaded little or not at all, be as moist as can reasonably be handled. Also, medium gluten flour works better than high gluten bread flour for this. A dough rolled flat should produce a reasonable rim as long as the edge is kept clear. A hand stretched dough will be naturally thicker toward the edge; if you want a larger rim on a rolled crust, you can bunch up the edge a bit or even roll it over a bit; yeast doughs will heal very fast. It will puff more in a very hot oven.
I found that my pizza dough started puffing up more when i ditched my rolling pin and instead stretched it by hand and/or on the counter.
You could always get to the point of preparation and then have a situation that requires you to leave the house for the night and not be able to bake your pizza until the next day. Happened to me and I was amazed and how much more the crust puffed after an extra day in the fridge (I always do a slow rise in the fridge - usually just overnight. In this case, the dough sat in the fridge and extra day).
Problem is that stretching pizza dough using a rolling pin pushes out all of the medium and small sized gas bubbles (CO2) and air pockets from the kneading process that will eventually expand in the oven to create that classic crisp but sponge-like cavernous airy crust.
I recommend: 1) Allow the yeast in your dough to slow ferment for at least 24 hours in the fridge before baking 2) Make sure the dough isn't overkneaded - stop when the dough first arrives at near the right texture/consistency and leave it be 3) Stretch by hand or on the counter like Daniel suggests, 4) Turn your oven up as hot as it can possibly go (500F is the sweet spot for most home ovens, especially gas ones) 5) PREHEAT your pizza stone in the oven before baking on it (I recommend unglazed quarry tiles too). 6) When topping your pizza, try to use a pizza sauce with as little water as possible (if making homemade sauce from canned whole tomatoes, drain ALL of the juice in the can before cooking) and go easy on the veggies (they can be added to the hot pizza either just before taking out of the oven or immediately after, they will warm up quickly).
Source: Making a lot of pizzas for myself in my gas oven at home.
I don't know where the notion that rolling the dough somehow brutalizes it comes from; I've rolled a million pizza crusts ; I can't swear I've never popped a bubble, but I can't swear I have, either. It certainly doesn't behave like bubble wrap, as some seem to think. Hand stretched pizza crusts are usually thicker at the rim, which is OK, but they're also thicker as you approach the rim, which I don't like. Most gas ovens in my (limited) experience go to 550 degrees, but don't have a limit on broil, so can be pushed to higher temps. I use an outdoor oven with a stone in the summer, but in the winter I find that a perforated pizza pan at the bottom of the oven works very well, and doesn't require the extensive preheating times a stone does.
If you can, get a pizza steel to augment the hot oven. Double check your yeast's expiration date. And cheat--I add about a third more yeast than called for before I cold ferment the dough.
Marcmarc, in case you aren't aware of it, the pizza steel Maryann refers to is also called the Baking Steel. I love mine! Check out their website at baking steel.com. There may be other manufacturers, but this was the original. I got mine from King Arthur, made by Baking Steel.
I use Smitten Kitchen's lazy pizza dough, recipe on her site. It is very easy to throw together and rises beautifully and blistery in the oven!