Step 1Place a pizza stone in the oven and heat the oven to 500 degrees, or as high as your oven goes, for at least 30 minutes. If you have refrigerated the dough, remove it from the refrigerator and let it sit at room temperature for 5 to 10 minutes.
Step 2Place the first ball of dough on a lightly floured work surface or a floured peel. Sprinkle a little more flour on top of the ball. Using your fingertips, press the dough ball evenly into a large, flat disk about half an inch thick. Now either use a rolling pin or stretch the dough out by hand, pizza-parlor style. There is no shame in rolling out pizza dough. But before you begin rolling, make sure you've pressed a little extra dough toward the outside edge to ensure a thicker rim, which will offer a satisfying chew, and a thinner center.
Step 3If working with your hands, flatten the ball with your hand, then press from the center out until it is about 6 inches in diameter. Now, from the outside in, working around the rim in concentric circles, gently tug the dough, using the same gesture you would to snap a wrinkle out of jeans while hanging them on a laundry line, except delicately. If the dough tears, knead it back together, set it at the end of the assembly line to relax, and work the next ball of dough more gently. If the dough is twitchy and keeps snapping back, cover it with a slightly damp towel and let it rest for 5 minutes. The glutens will relax.
Step 4After stretching the dough evenly all around, lift it and lay it over the back of the fist of one hand. It should be flopping. Place your other fist underneath the dough so your fists are almost touching. Now gently stretch the dough by moving your fists away from each other; each time you perform this stretching move, rotate the dough. Continue stretching and rotating until the round of dough is about 1/4 inch thick and measures about 10 inches across.
Step 5Lay the extended dough on a floured peel. (The flour will keep it from sticking as it goes into the oven.) Spread about 1/2 cup of sauce over the dough, then dot the surface evenly with slices of mozzarella. Sprinkle 1 tablespoon Parmesan cheese on top.
Step 6Opening the oven door quickly, put the peel at the outside edge of the pizza stone and, with a short jerk, slide the dough off the peel and onto the stone. Don't overdo it or the dough will end up in a curled mess at the back of the oven.
Step 7Bake for 10 to 12 minutes. The pizza is done when the crust is toasty-smelling and is a deep golden brown with dark spots.
Step 8Remove the pizza from the oven with the peel or a spatula. Slice and serve the first pizza, take requests for special toppings on the next one and begin production again. Note that the longer the oven is on, the hotter the pizza stone gets. The third and fourth pizzas may cook faster than the first one.