Make the biga: Place the flour and yeast in a bowl. Add the water and stir with a wooden spoon for 2 minutes; the mixture will be soft and sticky. Cover with plastic wrap and let rise at room temperature 2 to 24 hours (ideally 12 hours).

Make the dough: Combine the flour with the yeast and salt in a large bowl. Mix well with a wooden spoon. Add the biga and enough warm water to form a soft dough that holds together and forms a mass around the wooden spoon.

Knead vigorously for 8 minutes, or until smooth and supple and elastic, adding as little flour as possible. Shape into a ball. Place in a lightly floured bowl (or a lightly floured freezer bag), cover with plastic wrap, and let rise at cool room temperature for 2 hours, or until doubled in bulk.

Turn the dough out on a very lightly floured counter and knead for 1 minute. This redistributes the yeast throughout the dough and makes for a lighter schiacciata.

Return to the bowl (or freezer bag) and cover with plastic wrap. Let rise at cool room temperature until doubled again, about 1 and ½ to 2 hours.

Meanwhile, preheat the oven with a baking stone in it to 425 degrees (preferably set on convection). Line 2 baking sheets with parchment paper.

To bake: Combine the olive oil, water, salt, and rosemary in a bowl and mix well with a fork.

Turn the risen dough out onto a lightly floured counter. Without deflating it, cut it into 2 pieces and place each on one of the prepared baking sheets. Working delicately so as to avoid deflating the air bubbles in the dough, flatten each piece of dough into an even rectangle. Dimple with your fingertips (this prevents excessive ballooning in the oven). Pour on the water-olive oil mixture, dimple again with your fingertips, and let rest for 20 minutes.

Place one of the baking sheets gently on the baking stone. Bake for 20 minutes, or until the schiacciata is golden brown and crisp. Repeat with the second schiacciata, allowing the oven a few minutes to come back up to temperature after unloading the first schiacciata.

Serve hot, warm, or at room temperature, or freeze in plastic freezer bags and reheat for 15 minutes in a preheated 350 degree oven.