Combine flour, water, yeast, salt, and olive oil in the bowl of a stand mixer. Mix with the paddle attachment for 30-45 seconds, just until everything comes together in a shaggy dough. This can also be done by hand with a spoon by stirring for 1 minute. Scrape down sides of bowl to gather the dough into a rough ball, then cover loosely with a piece of plastic wrap and let it rest for 5 minutes.
After 5 minutes, use wet hands to stretch the dough out, pulling from the bottom, and laying it over the top of itself, sort of folding it in half. Rotate the bowl 90 degrees and repeat the motion of stretching the dough out and folding it on top of itself 3 more time for a total of 4 folds. If the dough is sticking to your hands, moisten them again or use a wet bowl scraper to scrape the dough away from the side of the bowl so you can pull the dough from the bottom. Cover and let rest for another 5 minutes.
Repeat the process of making the four folds, then covering and resting for the dough for 5 more minutes between each set of folds, three more times, for a total of four rounds of folding that take the place of kneading the dough. After that, cover with plastic wrap and let rest for 40 minutes at room temperature before sticking the dough in the fridge to slowly rise overnight. Let the dough rise at least 12 hours, but up to 72 to develop flavor.
Three hours before you want to serve the pizza, take the dough out of the fridge. Divide the remaining olive oil between two 10" or 12" cast iron pans (2 tablespoons per pan), swirling to coat the pans well and using your fingers to use some of the oil to grease up the sides a bit as well. If you don't have a cast iron pan, another oven-safe skillet, 10-inch cake pan, or even a 9x9-inch square baking dish will work.
Divide the dough between the two pans, turning to coat both sides with oil. Gently press the dough towards the edges of the pan, dimpling it with your fingers as you do so. If the dough shrinks back, that's okay. Let it rest for 15 minutes, then stretch it again until it reaches the sides of the pan. If it still doesn't reach the edges, give it a final 15 minutes rest and then stretch it one more time.
Cover the crust loosely with a piece of plastic wrap and let it rise at room temperature for 2 hours. 30 minutes before baking, preheat the oven to 550 degrees F (or as hot as your oven will go).
Top each pizza with about ½ to ¾ cup of pizza sauce, spreading it all the way to the edges of the crust. Sprinkle with the shredded mozzarella cheese all the way to the edges of the pizza to create a caramelized edge crust. Top with the your favorite toppings and sprinkle each pizza with parmesan cheese.
Bake on the bottom rack of the oven for 12 to 15 minutes until the cheese is bubbling and the bottom and edges of the crust are golden brown. You can use a metal spatula to lift and check the bottom. If your oven doesn't go all the way to 550 degrees F, you will need to increase the baking time to more like 18 to 20 minutes for a lower temperature like 450 degrees F.
Run a knife around the edges to keep the cheese from sticking as it cools, but let the pizzas rest for 2 minutes. Use a metal spatula to slide the pizzas out of the pans onto cooling racks so the crust stays crisp. If you leave the pizzas in the pan too long, the crust will start to go soggy. Slice and serve.