I was telling a friend how to do it. It's surprisingly easy:
(11:31:24 AM) Me: okay
(11:31:38 AM) Me: so, make pizza dough. It's easiest if you have a food processor
(11:32:08 AM) Me: you put flour, yeast, salt into food processor and turn it on, pour in enough water that it starts to turn to the right consistency
(11:32:14 AM) Me: the food processor will knead the dough for you
(11:32:23 AM) Me: so then you've got your dough
(11:33:03 AM) Me: now take your cast iron skillet, give it a quick wipe down with a paper towel, then pour some oil in it and grease it by rubbing another paper towel over it
(11:33:18 AM) Me: put the dough in there and shape it to fit the bottom of the pan, and up along the sides
(11:33:33 AM) Me: heat up the oven high, like 525 F if you can
(11:33:46 AM) Me: put it in for five minutes after preheating to let the dough bake a bit on all sides
(11:34:19 AM) Me: then take it out, put in cheese, then some sauce, then toppings, then more sauce maybe mixed with a bit more cheese, until it's as high as you want it
(11:34:25 AM) Me: put it back in and bake for 15 mins
(11:34:40 AM) Me: take it out and whammo, chicago style pizza
(11:34:49 AM) Me: just use a knife to cut it straight inside the pan
(11:34:58 AM) Me: the cast iron can take it
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It's easy to make vegan too, if you make a "ricotta" out of tofu. Thoroughly wash your hands, and then squish the tofu between your fingers and doing that until it's basically ricotta texture. Add salt, nutritional yeast (NOT bakers yeast), oregano, and basil. Use that instead of normal cheese.
It'll be ricotta-like. If you want something cheesier that's still vegan, I recommend Daiya as a faux-cheese brand.
@Sumana Harihareswara I accidentally used way too much flour so I'm not really sure what the right amount would be. For my 10 inch skillet, I'd probably try two cups total of flour next time. But anyway, I used the ratio of 3/4 cup all purpose flour + 1/4 cornmeal + 1 tbsp olive oil + 1 tsp salt. Use that as your baseline, then multiply as needed to fit the pan.