Use this dough to make our Grilled Pizzas with Tomato, Avocado, and Pepper-Jack Cheese, as well as our Grilled Pizzas with Plums, Prosciutto, Goat Cheese, and Arugula.
Stir warm water, sugar, and yeast in a small bowl until yeast is dissolved. Let stand until foamy, about 5 minutes. Brush a large bowl with oil, and set aside.
Stir together the flour, cornmeal, and salt in a large bowl. Pour in the yeast mixture and the oil; stir mixture until all of the flour-mixture is incorporated. Continue to stir until a stiff dough forms. Turn out dough onto a lightly floured surface, and knead with floured hands, dusting with as little flour as possible if dough seems sticky, just until the ball becomes smooth, 2 to 3 minutes. Reshape the dough into a ball. (Alternatively, pour 5 cups all-purpose flour, cornmeal, the salt, yeast mixture, and oil in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until dough is smooth and slightly sticky to the touch, 2 to 3 minutes. If dough seems too sticky, add up to 1 cup flour, 2 tablespoons at a time, mixing after each addition. Knead 4 or 5 turns on a clean work surface to form a ball.)
Place dough in oiled bowl, smooth side up. Tightly cover with plastic wrap, and let rise in a warm, draft-free spot until doubled in bulk, about 40 minutes.
Remove plastic wrap; punch down dough. Fold dough back onto itself 4 or 5 times; leave smooth side up. Cover with plastic wrap; let rise again until doubled in bulk, 30 to 40 minutes.
Punch down dough, and transfer to a clean work surface. Cut dough with a bench scraper or knife into sixths. Knead each piece 4 or 5 turns to form a ball. Cover all but one with plastic wrap.
On a lightly floured work surface, flatten remaining dough ball into a disk. Loosely cover with plastic wrap; let rest 5 minutes. Using a rolling pin or your fingertips, flatten and push dough evenly out from center to form a 9-inch circle (or a 7-by-11-inch rectangle or rough oval).
Line a baking sheet with parchment paper, and sprinkle with flour. Place dough on top. Cover with another sheet of parchment, and sprinkle with flour. Roll out and stack remaining dough balls.
Wrap baking sheet with plastic wrap; refrigerate pizza dough until ready to use, up to 1 day.
Dough can be kept frozen up to 1 month (thaw in refrigerator before using).