Put the pizza stone in a gas oven on a rack about 8 inches from the broiler. Preheat the oven on bake at 500 degrees F for 30 minutes. Switch to broil for 10 minutes.
With the dough on the peel, spoon the Tomato Sauce over the surface and spread it evenly, leaving about an inch of the rim untouched. Distribute the mozzarella over the pie. Place the sausage in small mounds around the pizza. Arrange the mushrooms and onion evenly on top. Sprinkle evenly with the chili flakes and salt. With quick, jerking motions, slide the pie onto the stone. Broil for 3 1/2 to 4 minutes under gas (somewhat longer with an electric oven), until the top is bubbling and the crust is nicely charred but not burnt.
Using the peel, transfer the pizza to a tray or serving platter. Slice into wedges and serve immediately.
In a medium bowl, thoroughly blend the flour, yeast, and salt. Add the water and, with a wooden spoon or your hands, mix thoroughly. Cover the bowl with plastic wrap or a kitchen towel and allow it to rise at room temperature (about 72 degrees F) for 18 hours or until it has more than doubled. It will take longer in a chilly room and less time in a very warm one.
Flour a work surface and scrape out the dough. Divide it into 4 equal parts and shape them: For each portion, start with the right side of the dough and pull it toward the center; then do the same with the left, then the top, then the bottom. (The order doesn't actually matter; what you want is four folds.) Shape each portion into a round and turn seam side down (see Cook's Note). Mold the dough into a neat circular mound. The mounds should not be sticky; if they are, dust with more flour.
If you don't intend to use the dough right away, wrap the balls individually in plastic and refrigerate for up to 3 days. Return to room temperature by leaving them out on the counter, covered in a damp cloth, for 2 to 3 hours before needed. Don't freeze the dough, but you can store it in the refrigerator, wrapped in plastic, for up to three days. In effect, when you're set to use it, you have your own ready-made dough.
If using fresh tomatoes, bring 4 quarts water to a boil in a 5- to 6-quart pot.
Cut away the dry stem area of the tomatoes, leaving the core intact. Place 2 or 3 tomatoes at a time in the boiling water for 5 to 10 seconds. Remove with a slotted spoon and put on a rack to cool. Peel the tomatoes with a paring knife.
Whether using fresh or canned, cut each tomato into several wedges and run them through a food mill over a medium bowl to create a pulp (not a fine puree; you want to retain some texture). If you don't have a food mill, just squish them with your hands--it's messy but fun.
Stir in the olive oil and salt. The sauce will keep, covered, in the refrigerator for up to 1 week.
makes 620 to 800 grams (depending on whether you use fresh or canned tomatoes, which yield a greater volume); or enough for about 8 pizzas
While I'm not picky about the flour--either bread flour or all-purpose is fine--what does concern me is how the dough is handled. Treat it gently so the dough holds its character, its texture. When you get around to shaping the disk for a pie, go easy as you stretch it to allow it to retain a bit of bumpiness (I think of it as blistering), so not all of the gas is smashed out of the fermented dough. I prefer to hold off on shaping the ball until just before topping it. If it's going to sit for a while--more than a couple of minutes--cover it with a damp kitchen towel to prevent it from drying out. I offer you two approaches for shaping. The simpler one, executed completely on the work surface, is slower than the second, where you lift the disk in the air and stretch it by rotating it on your knuckles. Lifting it into the air to shape it is more fun, too. Shaping the Disk (Method 1): Take one ball of the dough and generously flour it, your hands, and the work surface. Then press it down and gently stretch it out to 6 to 8 inches. Very carefully continue the process, massaging it into a roundish disk of 10 to 12 inches, stroking and shaping with the palms of your hands and with your fingers. Don't handle it more than necessary, though; you want some of the gas bubbles to remain in the dough. It should look slightly blistered. Flour the peel and lift the disk onto the center. The dough is now ready to be topped. Shaping the Disk (Method 2): Take one ball of the dough and generously flour it, your hands, and the work surface. Then press it down and gently stretch it out to 6 to 8 inches. Supporting the disk with your knuckles toward the outer edge and lifting it above the work surface, keep stretching the dough by rotating it with your knuckles, gently pulling it wider and wider until the disk reaches 10 to 12 inches. Set the disk on a well-floured peel. It is now ready to be topped.
Reprinted with permission from My Pizza by Jim Lahey, Clarkson Potter copyright (c) 2012