Update 5/23/13: The rest of this post is the cheap and long way of grilling pizza. I no longer use this method because I am getting much better and faster results with the Kettle Pizza.
Grilling pizzas on the Weber Jumbo Joe is a snap once you figure out the basic strategy. The grill grate is too close to the charcoal to grill a pizza directly on the surface. You need to provide a shield against the direct heat as well as elevate the cooking surface away from the charcoal. I have had the best results grilling pizza on the Weber Jumbo Joe by placing an eleven inch rectangular aluminum pan (disposable) on the grill grate and resting a pizza stone on top of the pan.
All of my experiments have involved regular crust pepperoni pizzas. I have heard of folks grilling thin crusts directly on the grate but I don’t have any experience to share with that technique.
The pizza making part is the same as always. Roll out the dough, apply a layer of sauce and add toppings. I do this on a wooden cutting board that has been liberally dusted with corn meal so the pizza slides around very easily.
Pour a full chimney of lit charcoal into the Weber Jumbo Joe, place the aluminum pan on the grill grate and a pizza stone on top of the pan. Close the lid for about 10 minutes to let the stone get hot. Slide the pizza onto the pizza stone, close the lid and let the pizza bake for about 30 minutes. Both the top and bottom air vents should be completely open.
I found I had to use a large spatula as a backstop when sliding the pizza onto the stone. Before I figured this out it was pretty common for the pizza to slide off my cutting board so fast that it would overshoot the pizza stone and land in a crumpled pile on the grate. Grrrrr.
Any other arrangement I have tried has resulted in a pizza that was burnt on the bottom before the cheese had browned. This technique has always generated great results.
Be sure to check out some other Weber Jumbo Joe Upgrades!