3 tablespoons extra-virgin olive oil, plus more for brushing
1 cup (packed) minced yellow onion
2 medium garlic cloves, minced
1/4 cup finely chopped fresh basil
1 tablespoon minced fresh thyme
2 teaspoons minced fresh rosemary
Freshly ground pepper
1 1/2 cups lukewarm water (105° to 115°)
1 cup lukewarm milk (105° to 115°)
1 scant tablespoon table salt
2 teaspoons plus a pinch of sugar
One 1/4-ounce envelope dry yeast
About 6 1/2 cups bread flour
Cornmeal, for dusting
Coarse salt, for sprinkling
1/4 cup ice water
Heat the olive oil in a medium skillet over moderate heat. Stir in the onion and garlic, reduce the heat to low and cook until softened and fragrant, about 3 minutes. Add the herbs and a generous amount of pepper and cook for 1 minute. Transfer the mixture to a large bowl. Stir in 1 cup of the water, then the milk, table salt and 2 teaspoons sugar.
In a small bowl, dissolve the yeast and the pinch of sugar in the remaining 1/2 cup lukewarm water until creamy and starting to bubble. Add to the onion mixture. Stir in the flour, 1 cup at a time, just until the dough becomes too stiff to stir. Turn out the dough onto a lightly floured work surface. With the help of a dough scraper, knead in only as much additional flour as necessary to keep the dough from sticking. Knead the dough until smooth, supple and elastic, about 5 minutes.
Generously grease a clean large bowl with olive oil. Transfer the dough to the bowl and turn the bowl to coat with oil. Cover the bowl with plastic wrap and a kitchen towel. If desired, label the bowl to remind you when to punch down and shape the dough. Set aside in a warm draft-free spot until doubled in bulk, about 2 hours.
Punch down the dough. Re-cover the bowl and let the let the dough rise again until doubled, about 1 hour.
Brush olive oil over the bottom of a 17-by-13-by-1-inch black steel or heavy aluminum baking sheet. Sprinkle cornmeal on the pan, then tap out excess.
Punch down the dough and turn it out onto a cornmeal-dusted work surface. Turn the dough over and over to coat lightly with cornmeal and shape into a rough rectangle. Lift the dough and place in the prepared pan. Gently pull, push and pat the dough so it fills the baking sheet. Let the dough rise uncovered in a draft-free spot until billowy, 45 minutes to 1 hour.
Preheat the oven to 450° and position a rack in the bottom third. If using a baking stone or tiles, place on the rack and heat for 30 minutes.
Dip your fingers in flour and make many deep indentations in the dough. Brush lightly with olive oil and sprinkle with coarse salt.
Place the baking sheet in the oven, toss the ice water on the oven floor and bake the focaccia for about 30 minutes, until the edges are crisp and a deep golden color. Using a long metal spatula, slide the focaccia onto a large rack to cool. To serve, cut into pieces with a serrated knife.