Homemade pizza dough and sauce in my Lodge double Dutch oven lid and Darto carbon steel pan. The dough was cold fermented in the fridge then proofed in buttered pans. I cooked the dough on the stove top briefly to help it firm up before adding sauce and toppings.
For a crispier bottom, an alternative is to preheat the pans then add oil and (carefully) spread the proofed dough into the pan before adding toppings and cooking.
I've rarely had pizza or bread on cast iron stick. If a spot does stick then I scrape it clean with a metal scrubbing pad and the next pizza just ever so lightly brush a tiny bit of oil on and bake as usual.
Yep, it makes shaping to the pan easier (and safer), though I’m still working on getting a crispy crust with this method.
I used to proof it on the counter before dropping it into a hot, oiled pan, and that produces a great crispy bottom. This method is lazier, though, and with butter, the dough hasn’t stuck at all for me.
I’m using roughly this method, though with my own dough recipe.
I suspect my crust doesn’t come out as good because my oven has the heating element on top. The linked recipe suggests putting the pan on the bottom rack, which makes me think they assume a bottom heating element.
I preheat my pan on the stove with a little oil, then drop the dough in pre-shaped (folded to make handling easier.) The bottom cooks while I assemble the toppings, then I throw it under the broiler til the top is crispy. If you're going to do a cold pan, then I don't see why using cast iron is beneficial. It seems like it would just prolong the time in the oven, especially if you're only using a broiler element.