Makes dough for two 9-inch pizzas.
1 teaspoon yeast
1/2 cup plus 1 tablespoon warm water (105 to 110 degrees F)
1 1/2 cups bread flour or all-purpose flour
2 teaspoons granulated sugar
1 teaspoon salt
1 tablespoon extra virgin olive oil plus 1 tablespoon for coating
To Make The Dough
Dissolve the yeast in the water and set aside for 5 to 10 minutes. Be sure that the water is hot. Temperatures of 120 degrees F and above will kill the yeast, and your dough will not rise.
If using an upright electric mixer, such as a KitchenAid, use the mixing paddle attachment because the batch size is too small for the dough hook to be effective. Combine all other ingredients (except the additional teaspoon of olive oil) and combine them with the dissolved yeast in the mixing bowl. (Do not pour the salt directly into the yeast water because this would kill some of the yeast.) Allow these ingredients to mix gradually, use the lowest 2 speeds to mix the dough. Mix for 2 to 3 minutes, until the dough is smooth and elastic. Over-mixing the dough will produce tough, rubbery dough, and friction will cause the dough to rise too fast.
If using a food processor, using a dough "blade" made of plastic rather than the sharp steel knife attachment, which would cut the gluten strands and ruin the consistency of the dough. Otherwise proceed as above. Be especially cautious not to mix too long with a food processor because the temperature resulting from the friction of mixing could easily exceed 120 degrees F, killing the yeast. Mix only until a smooth dough ball is formed.
If mixing by hand, place the dry ingredients in a 4 to 6 quart mixing bowl. Make a well in the middle and pour in the liquids (reserving the teaspoon of olive oil). Use a wooden spoon to combine the ingredients. Once initial mixing is done, you can lightly oil your hands and begin kneading the dough. Knead for 5 minutes. When done the dough should be slightly tacky (that is, it should be barely beyond sticking to your hands).
Lightly oil the dough ball and the interior of a 1-quart glass bowl. Place the dough ball in the bowl and seal the bowl with clear food wrap. Seal airtight. Set aside at room temperature (70 to 70 degrees F) to rise until double in bulk - about 1 1/2 to 2 hours.
The dough could be used at this point, but it will not be that wonderful, chewy, flavorful dough that it will later become. Punch down the dough, re-form a nice round ball and return it to the same bowl. Cover again with clear food wrap. Place the bowl in the refrigerator overnight, covered airtight.
About 2 hours before you are ready to assemble your pizza, remove the dough from the refrigerator. Use a sharp knife to divide the dough into 2 equal portions (or 4 equal portions if making appetizer-size pizza or if smaller 6-inch pizzas are desired.)
Roll the smaller doughs into round balls on a smooth, clean surface. Be sure to seal any holes by pinching or rolling.
Place the newly-formed dough balls in a glass casserole dish, spaced far enough apart to allow for each to double in size. Seal the top of the dish airtight with clear food wrap. Set aside at room temperature until the dough balls have doubled in size (about 2 hours). They should be smooth and puffy.
To stretch and form the dough for pizza
Sprinkle a medium dusting of flour over a 12 x 12-inch clean, smooth surface. Use a metal spatula or dough spacer to carefully remove a dough ball from the glass casserole dish, being very careful to preserve its round shape. Flour the dough liberally. Place the floured dough on the floured smooth surface.
Use your hand or rolling pin to press the dough down forming a flat circle about 1/2-icnh thick. Pinch the dough between your fingers all around the edge of the circle, forming a lip or rim that rises about 1/4-inch above the center surface of the dough. You may continue this outward stretching motion of the hands until you have reached a 9-inch diameter pizza dough.
To dress the pizza
Lightly sprinkle cornmeal, semolina or flour over the surface of a wooden pizza peel. Arrange the stretched dough over the floured peel surface. Work quickly to dress the pizza so that the dough will not become soggy or sticky from the sauces and toppings.
When you are ready to transfer the pizza to the pizza stone in the pre-heated oven, grasp the handle of the peel and execute a very small test jerk to verify that the pizza will come easily off the peel. If the dough does not move freely, carefully lift the edges of the dough and try to rotate it by hand. Extreme cases may require that you toss more flour under the dough edges.
Once the dough is moving easily on the peel, open the oven and position the edge of the peel over the center of the stone about 2/3 from the front of the stone. Jiggle and tilt the peel to get the pizza to start sliding off. When the pizza begins to touch the stone, pull the peel quickly out from under it. Don't attempt to move the pizza until it has begun to set (about 3 minutes). The peel can be slid under the pizza to move it or remove it.