Step 1
Make the dough: Combine the flour, sugar, salt and yeast in the bowl of a stand mixer (see Tips). Whisk together to combine, then add the water and oil. Mix at low speed with the dough hook attachment, stopping occasionally to scrape down the sides of the bowl with a rubber spatula, until the dough comes together in a shaggy ball. Cover the bowl and let the dough rest for 10 minutes. Mix on medium-low speed until the dough is silky and pulls away from the sides of the bowl, about 5 minutes. Transfer the dough to a lightly floured work surface.
Step 2
Using lightly floured hands, shape each piece into a smooth ball, then lightly coat each with oil, using your hands to cover every surface. Transfer ball to a quart-size zipper-lock bag or other sealable container at least three times its volume. (Quart-size plastic deli containers also work for this.)
Step 3
Ferment the dough: For good results, let the dough rest at room temperature until doubled in volume, about 3 hours. For better results, refrigerate the dough overnight. For best results, refrigerate the dough for at least 3 and up to 5 days.
Step 4
The day before baking, roll the dough: Transfer one dough ball to a work surface generously dusted with semolina or cornmeal. (Refrigerated dough can be rolled straight out of the fridge, though allowing it to rest covered for 1 hour at room temperature will make rolling easier.) Using a rolling pin, roll the dough into a very thin circle, lifting and rotating it occasionally (use a ruler or measuring tape to ensure the right size). If the dough feels like it keeps bouncing back as you try and stretch it, cover it with an inverted bowl or a clean kitchen towel, let it rest for half an hour, then try rolling again.
Step 5
Cure the dough: Transfer the dough to a flat surface lined with parchment paper or butcher paper. Allow to rest uncovered at room temperature overnight. The top surface of the dough should end up dry to the touch with a leathery feel. If they puff at all during curing, you can push any bubbles with a fork and push them down to flatten them.