Make the dough: In a large bowl, whisk together the flour, yeast, and salt. Add the water and 1 tablespoon olive oil and use a spoon or dough whisk to bring it together, stirring the mixture a few times to ensure there are no unmixed pockets of flour. Cover the bowl with plastic wrap and let it rise until it doubles and moves a lot when jiggled, about 1 ½ to 2 hours at room temperature.

Assemble the pizza: Heat your oven to 450°F (230°C). Coat a 12-inch (30-cm) round cast-iron skillet with 3 tablespoons olive oil. Scrape dough into the pan, then turn it over once so it’s oiled on both sides. Dip your fingers in the oil to coat them and dimple the dough out to the edges as best as you can; it’s okay if it doesn’t fully stretch at this point. Set it aside, loosely covered, for 30 minutes to finish proofing.

To assemble: Spoon the sauce generously over the dough, covering it all the way to the edges of the pan. Sprinkle with mozzarella, then pecorino or parmesan. Season as you wish with salt, pepper flakes, and oregano, then drizzle a final tablespoon of oil over the top before transferring it to the oven.

Bake the pizza: For 30 minutes, until deeply golden brown at the edges and toasty on top.

To serve: Scatter with fresh basil. You can serve it right in the pan, but I prefer to protect my knives. Loosen the pizza from the pan and slide it onto a cutting board before cutting it into wedges.

Do ahead: Leftovers reheat fantastically. I heat leftover slices on a foil-covered sheet pan at 350°F or 375°F for 5 to 10 minutes.