Prepare the sponge: the night before you bake, stir together the water and yeast until the yeast dissolves. Add the flour and knead briefly by hand until a shaggy dough forms. Transfer to a small bowl or jar where the sponge touches the sides yet has some room to grow vertically. Cover with plastic wrap and let sit at cool room temperature overnight (12-14 hours).

Make the dough: The next day, dissolve the yeast in 2 tablespoons lukewarm (not hot) water in small bowl. In the bowl of a stand mixer with a hook attachment combine sponge, flour, sugar and 1 cup plus 2 tablespoons very cold water. Mix on low speed until a shaggy mass forms, then raise to medium speed and knead for about 5 minutes.

Add the olive oil and the yeast-water mixture and continue to knead for another 5 minutes. Add the remaining 1 tablespoon of water and continue to knead until the dough is smooth and elastic, 5 to 10 more minutes.

Lightly flour a clean work surface and turn the dough out onto it. Using a bench scraper or large knife, divide the dough in half. Slightly stretch and flatten one portion into an oblong shape, then fold into thirds. Rotate the dough 90 degrees, stretch, and fold into thirds again. Gently stretch the dough into a rounded brick shape and set aside, seam-side down. Repeat with the second half of the dough. Lightly flour the tops of the two loaves, then cover with a clean, dry kitchen towel or plastic wrap. Set aside to rest at room temperature until doubled in size, about 30 minutes.

Prepare the pans: Pour 2 tablespoons of olive oil in the center of each baking sheet and spread with your fingers to grease the bottom of the sheets, leaving a 2-inch border around the edge ungreased. Gently roll out each dough with a flour-dusted rolling pin to a thickness of about ½ an inch, and transfer both doughs to the oiled sheets. Cover sheets with a clean dish towel or plastic wrap and let rise in a draft-free place for 20 to 25 minutes.

Proof in pans: Uncover, dust lightly with flour, and gently stretch the dough to the ungreased edges of the pan. Press the dough into the edges of the pan with your fingertips, creating a seal so that the brine won’t seep under later. Cover and set aside to rise for 1 hour to 1 hour and 15 minutes.

For the brine: Stir together hot water and salt until the salt is completely dissolved. Uncover the dough and test with your finger; if it springs back when you make a firm indentation in the dough, it’s not ready yet. Cover and let proof a little longer until the indentation remains when firmly pressed. Sprinkle the surface with a bit of flour. Use your fingers to create dimples in the dough, then pour half of the brine over the dough in each tray and sprinkle each with 2 tablespoons of olive oil. Let proof again for 40 to 45 minutes uncovered.

Bake: Preheat the oven to 450°F with one rack placed in the upper third and one placed in the lower third of the oven. When the oven is hot, bake the focaccia for 15 to 18 minutes, rotating trays between the top and bottom racks and turning them back to front halfway through cooking time. The focaccia is ready when it is golden, but the dimples are still light beige. Remove from oven and brush immediately with olive oil. Remove from the baking sheet immediately and let cool upside down.