Make the Pizza Dough: Place the flour, salt, yeast, and sugar in the bowl of a stand mixer fitted with a dough hook attachment; mix on low speed to combine. Add the water and knead on low speed until the mixture comes together in a rough dough and no dry flour remains. Allow the dough to rest for 10 minutes. Continue kneading on low speed for an additional 10 minutes. The dough should be soft, elastic and slightly tacky. If the dough is sticking to the bowl, add more flour 1 tablespoon at a time until it clears the sides and is barely sticking to the bottom. Cover the bowl tightly with plastic wrap and refrigerate for at least 8 and up to 72 hours.
Transfer the dough to a floured work surface and dust the top with additional flour. Using a bench scraper, divide the dough into six even pieces (they should be about 6 ounces each). Shape each piece into a ball. Coat six small bowls with non-stick cooking spray and add one dough ball to each bowl. Turn to coat the ball, then cover the bowl tightly with plastic wrap and allow to rise at room temperature for 2 hours.
Prepare the Sauce: Place the olive oil and garlic in a medium saucepan over medium heat. When the garlic begins to sizzle, add the tomatoes. Simmer, uncovered, stirring occasionally, until the sauce is thickened, about 15 minutes. Season with salt and pepper. (Note: You can simply mix the ingredients together in a bowl if you are short on time, but the sauce will not be as thick.)
Transfer 1 ball of dough to a bowl filled with flour and turn to coat. Dust off excess flour and transfer to a floured work surface. Gently stretch the ball of dough into a 10-inch circle, leaving the outer 1-inch edge slightly thicker than the center.
Bake the Pizzas: Preheat the broiler to high and arrange the oven rack so that a 12-inch cast iron skillet (or other heavy-bottomed 12-inch skillet) just fits underneath the broiler.
Dust the skillet with flour, tap out excess, then heat the skillet over high heat for 3 minutes. Transfer the 10-inch round of dough to the skillet (it should cover the entire bottom surface). Spread some sauce evenly over the dough, leaving the outer 1-inch border un-sauced. Top with slices of the cheese and sprinkle with fresh basil. Transfer the skillet to the oven and broil until the pizza is puffed and darkly charred in spots. Return the skillet to the stovetop and cook until the bottom is darkly charred in spots (depending on your pan, you may be able to skip this step if the bottom is already browned after removing from the oven). Transfer the pizza to a cutting board and serve. Repeat steps 4 through 6 to bake remaining pizzas.
Notes
Note #1: You can purchase Italian "00" flour from Amazon or King Arthur Flour. If you need to substitute, you can use bread flour or all-purpose flour, but the flavor and texture will not be the same.Note #2: If you don't have a cast iron skillet, I would probably recommend using a baking stone under the broiler so you could still get that crisp bottom crust.Note #3: I froze the unused portions of dough after step #2 (wrapped in plastic wrap and placed in a ziploc freezer bag), then thawed in the refrigerator overnight and allowed it to sit at room temperature for 30 minutes before working with it.Nutritional values are based on one serving