Measure 3 c. of warm water. Put 1/2 tsp. (2 grams) of yeast in a separate, small container. Add about 3 tablespoons of the water to the yeast and set aside.
Combine all the flour and the remaining water in a 12-quart round tub. Mix by hand just until incorporated. Cover and let rest for 20 to 30 minutes on your counter.
Sprinkle the salt over the top of the dough. Stir the yeast mixture with your finger; then pour it over the dough. Use a small piece of the mixture to wipe the remaining yeast goop from its container, then throw it back in the tub.
Mix by hand, wetting your working hand before mixing so the dough doesn’t stick to you. (It’s fine to rewet your hand three or four times while you mix.)
Reach underneath the dough and grab about one-quarter of it. Gently stretch this section of dough and fold it over the top of the other side of the dough. Repeat three more times with the remaining dough, until the salt and yeast are fully enclosed.
Pince the dough the pincer method (Using a pincerlike grip with your thumb and forefinger, squeeze big chunks of dough and then tighten your grip to cut through the dough so you can get all the ingredients really incorporated). 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.), alternating with folding the dough to fully integrate the ingredients. Do this for 5 minutes. Let rest for 30 minutes.
Fold the dough by grabbing the edges and stretching them up and into the center. Fold about 4 times.
Then lightly coat the dough and the bottom of the tub with olive oil to help prevent sticking. Let it rest, covered at room temperature, for 5-6 hours, or until doubled. When the dough is about double its original volume, it’s ready to be divided.
Divide. 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 6 equal-size pieces with a dough knife or plastic dough scraper.
Shape the dough into 6 balls. Shape each piece of dough into a medium-tight round, working gently and being careful not to degas the dough.
Put the dough balls on a lightly floured baking sheet, leaving space between them to allow for expansion. Lightly oil or flour the tops, cover with plastic wrap, and let rest at room temperature for 30 minutes.
Refrigerate for at least 30 minutes to make the dough easier to shape.
To prep for the pizza put the pizza stone in the oven and heat to 550°F or the hottest your oven will go (heat it on the BAKE feature, not broil). (If it only goes to 500°F that's fine, you'll just bake it a little longer.)
Pulse all sauce ingredients quickly in a blender. It doesn't need to be too finely pureed.
Remove the dough ball from the refrigerator, put it on the floured work surface and gently pat it down a bit to coat the bottom with flour. Leaving about 1 inch of the outer rim undeflated to be your crust, punch down the middle, then flip the dough over and repeat.
Gently stretch and turn the dough repeatedly, still letting the bottom of the dough pull down, expanding the surface. Keep a close eye on the thickness of the dough. You want it thin, but you don’t want it to tear or develop holes. If you end up with a small tear, don’t panic – it’s OK to patch it.
Spread the dough on the floured pizza peel and run your hands around the perimeter to shape it into a round and work out the kinks. Shake the peel to make sure your dough doesn't stick to it.
Add pizza toppings. Slide dough off pizza peel into oven (onto pizza stone - leave stone in the oven). Bake for 5-6 minutes at 550 (if your oven only goes to 500, bake for 7-8 minutes), or until tops of crust and cheese are browning.
Remove with pizza peel and transfer to a cool surface (we use a large cutting board or baking sheet). Let rest for 5 minutes before cutting and serving.