2. Combine the flour, semolina or cornmeal, and salt in large mixing bowl. Stir in the olive oil. Stir in the yeast mixture and then slowly add remaining water until the dough is stiff and sticky. Turn the dough onto lightly floured board and knead until it is smooth, moist, and elastic, about 10 minutes. Transfer to an oil-lined bowl, cover with damp towel, and let it rise in a warm place until doubled, 1 to 2 hours.
3. Punch down the dough once or twice and turn it out onto a lightly floured board. Cut it into 6 pieces for individual pizzas. Gently knead each piece into a ball. If baking soon, cover with towel and reserve on board. To store, tightly wrap each piece in plastic and store in the refrigerator for up to a day or in the freezer for 2 months.
Making the dough with a food processor (for large size processor):
1. Combine the 1/2 cup of the water, sugar, and yeast in a small bowl. Let the mixture rest until it is foamy, about 5 minutes.
2. In a processor fitted with the plastic dough blade, combine the flour, semolina or cornmeal, and salt. Pulse a few times to combine. Add the oil and briefly process.
3. With the machine running, add the yeast mixture through the feed tube. Slowly pour in the remaining water just until the dough clears the sides of the bowl and forms a ball on top of the blade. Process for an additional minute. Remove the dough and knead on a floured board about 1 minute. Follow 'hand' instructions for rising.
Making the pizzas:
4. Preheat the oven to 500°F or heat the grill to medium.
5. On a well floured counter, roll the 6 pieces of dough out with a rolling pin into 6 or 8-inch rounds.
6. If you are grilling the pizzas, grill the pizza rounds until they are golden on both sides.
7. Have everyone put their favorite toppings on their pizza.
8. To finish grilling the pizzas, put them back on the grill and cook with the cover down to warm the toppings for 2 or 3 minutes. Or, bake the pizzas on baking sheets in the oven until the crust is golden brown, about 15 minutes.
9. Cut into slices and serve.