FOR THE DOUGH: In a small bowl, dissolve the yeast in the water and let stand for 10 minutes.
In a large mixing bowl, combine 3 cups flour and the salt. Make an indentation in the center and pour in the yeast mixture and the oil. With a wooden spoon, beat the ingredients together to form a dough. Turn the dough out onto a floured surface and knead until smooth and elastic, adding more flour if necessary.
Form the dough into a ball, place it in a lightly oiled bowl, and cover with a damp cloth. Place the dough in a warm place and allow it to double in bulk, about 2 hours.
Punch down the dough and knead it for 3 or 4 minutes. Divide the dough into 2 equal pieces. On the floured surface, shape each piece of dough into a flat 10 x 5 inch rectangle. Transfer the dough to 2 oiled 10 ½ x 15 ½ inch (or larger) baking sheets. With the tips of the fingers, push “dimples” into the surface of the dough. Cover the dough and let rise again until doubled in bulk, about 1 hour.
Preheat the oven to 400°F Place the baking sheets in the oven and bake breads until the edges of the dough are lightly browned, about 15 minutes. (Can be made a day in advance up to this point; slide the dough onto wire racks to cool, wrap tightly in plastic wrap, and refrigerate. Or make well in advance, wrap well, and freeze.).
FOR TOPPING ONE, first brush the crust liberally with olive oil. Sprinkle 3 tablespoons Parmesan over the crust. Scatter about two thirds of the onion rings over the crust, arrange the tomato slices in a single layer over the onion, and top with the remaining onion rings. Sprinkle the thyme and basil over the tomatoes, followed by the remaining Parmesan and a few grindings of black pepper.
FOR TOPPING TWO, first brush the crust liberally with olive oil. Scatter the mozzarella over the crust and then arrange the strips of red pepper on top. Scatter the olives, garlic, fennel, and sage and add a few grindings of black pepper.
Bake the assembled focaccia for about 15 minutes, or until the edges of the crusts are well browned. Serve warm or at room temperature. (The focaccia can be baked 1 day in advance, wrapped tightly, and stored in a cool place—not refrigerated. Bake them in a hot oven for 5 minutes or so to refresh them.) Cut into small rectangles to serve. Makes two 10 x 15 inch flat breads.
John Hadamuscin’s Enchanted Evenings.