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Step 1
Measure and combine the ingredients: Using your digital scale, measure 350 grams of 90 to 95 degree F water into a 6-quart dough tub or large mixing bowl. Measure 15 grams of fine sea salt, add it to the water, and stir or swish it around in the tub until it is dissolved. Measure 0.3 gram (about 1/3 of 1/4 teaspoon) of instant dried yeast. Add the yeast to the water, let it rest there for a minute to hydrate, then swish it around until it’s dissolved. Add 500 grams of to 00 flour to the water-salt-yeast mixture.
Step 2
Mix the dough: Mix by hand, first by stirring your hand around inside the dough tub or bowl to integrate the flour, water, salt, and yeast into a single mass of dough. Then using your thumb and pointer finger, squeeze big chunks of dough, tightening your grip to cut through the dough. Do this repeatedly, working through the entire mass of dough. With your other hand, turn the tub while you’re mixing to give your active hand a good angle of attack. Then fold the dough back into a unified mass. Continue for just 30 seconds to 1 minute. The target dough temperature at the end of the mix is 80 degrees F; use your probe thermometer to check it.
Step 3
Knead and rise: Let the dough rest for 20 minutes, then knead it on a work surface with a very light dusting of flour for about 30 seconds to 1 minute. The skin of the dough should be very smooth. Place the dough ball seam side down in the lightly oiled dough tub or large mixing bowl. Cover with a tight-fitting lid. Hold the dough for 2 hours at room temperature (70 to 74 degrees) for the first rise. This timeline is flexible, so if you need to do this after 1 hour or 1-1/2 hours, don’t stress, just make up your dough balls a little early and add the difference in time to the next stage.
Step 4
Shape: Moderately flour a work surface about 2 feet wide. With floured hands, gently ease the dough out of the tub. With your hands still floured, pick up the dough and ease it back down onto the work surface in a somewhat even shape. Dust the entire top of the dough with flour, then cut it into 4 equal-sized pieces. Use your scale to get evenly sized dough balls. Shape each piece of dough into a medium-tight round, working gently and being careful not to tear the dough.
Step 5
Second fermentation: Place the dough balls on lightly floured dinner plates or a baking sheet, leaving space between them to allow for expansion. Lightly flour the tops and cover airtight with plastic wrap, and let rest at room temperature for 6 hours for the second fermentation. Alternatively, you can rest the dough balls for 4 hours at room temperature, and then refrigerate to hold for up to the next evening.
Step 6
Without refrigeration, the dough balls can be used anytime in the 4 hours following the second fermentation. If you refrigerated the dough balls, let them come to room temperature for an hour while you preheat the oven and prepare your toppings.
Step 7
Pour the entire contents of the can of tomatoes into the blender. Add the sea salt and pulse on the lowest speed setting very, very briefly, just until the tomatoes are blended.
Step 8
If you have refrigerated your dough overnight, remove your dough balls from the refrigerator about 60 to 90 minutes before baking pizza. Put your pizza steel or stone on an upper rack in your oven no more than 8 inches below the broiler. Preheat the oven to 550°F for 45 minutes.**
Step 9
Set up your pizza assembly station. Give yourself about 2 feet of width on the countertop. Moderately flour the work surface. Position your pizza peel next to the floured area and dust it lightly with flour. Have the sauce, oil, cheeses, and basil at hand, with a ladle or large spoon for the sauce. Switch the oven to broil 10 minutes before loading the pizza.
Step 10
To shape the pizza, put the dough ball on the floured work surface and flip to coat both sides. Leaving about a ½ inch of the outer rim un-deflated, punch down the middle with your fingertips, pushing the air toward the rim of the disk, then flip the dough over and repeat. Using floured hands, grab the rim at about the 10 o’clock and 2 o’clock positions and lift so the crust hangs down vertically; preserve the outer rim by placing your thumbs about a 1⁄2-inch from the edge. Let gravity pull the rest of the dough down to stretch it. Run the rim between your hands, working all the way around the circumference of the dough a couple of times.
Step 11
At this point, you can work as slowly as you want. If the dough gets sticky, set it down and give both the top and the bottom another dusting of flour. Next, make two fists and position them just inside the rim, with the crust still hanging vertically. Gently stretch and turn the dough repeatedly, letting the bottom of the dough pull down, expanding the surface. Keep a close eye on the thickness of the dough. There is no benefit to overstretching it-- when it's done, it's done and then you lay it onto the flour-dusted peel. You want the dough thin, but not so thin that it tears or can't support the weight of the toppings. If you end up with a small tear, don't panic-- it's okay to patch it by folding a small bit of dough over the hold.
Step 12
Transfer the disk of pizza dough to a floured peel and run your hands around the perimeter to relax it and work out the kinks.
Step 13
Spread the 1/4-1/3 cups of the tomato sauce over the dough to within ½ inch of the edge, smoothing it with the back of the spoon or ladle. Turn off the broiler, then gently slide the pizza onto the pizza stone or steel. Close the oven door and change the setting to bake at 550°F. Let the pizza bake for about 4 minutes, until the rim is just starting to turn golden. Use a pair of tongs or the pizza peel to remove the pizza onto a plate or cutting board. Drizzle a spoonful or so of olive oil on top of the pizza, then sprinkle 1/4th of the grated pecorino or parm evenly over the sauce. Layer 1/4th of the mozzarella and 3-5 basil leaves evenly over the pizza. Using your hands or the pizza peel, place the pizza back onto the pizza steel or stone and continue baking for 1 to 2 minutes.
Step 14
Change the oven setting from bake to broil and let the pizza bake until the cheese is softly melted and the crust is golden with spots of brown and a few small spots of char, about 2 minutes (check it after 1 minute to be safe). Use tongs or a fork to slide the pizza from the pizza steel or stone onto the plate. Drizzle a small amount of extra-virgin olive oil over the pizza and serve whole or sliced in half. Serve and eat immediately.