Shape and dimple the dough in a 12 by 17-inch (30 by 43-cm) sheet pan using the 2 tablespoons olive oil for preparing the pan and the 1/4 cup olive oil for dimpling the dough. Let the dough rise at room temperature for 2 to 3 hours, or until it fills the pan.
While the dough is rising in the pan, prepare the potatoes. If using new potatoes, place them in a saucepan with water to cover, bring to a boil, and boil for about 10 minutes, or until they can be easily pierced with a fork. Drain, let cool (or plunge them in cold water to speed the process), and cut into 1/4-inch-thick (6 mm) slices. If using regular-sized Yukon Gold potatoes, slice them paper-thin using a food processor, a mandoline, or a chef's knife. In a bowl, combine the sliced potatoes, onion, if using, and rosemary. Pour in the herb oil and toss gently to coat.
Preheat the oven to 500°F (260°C). When the focaccia is fully risen and ready to bake, remove the potatoes from the oil, shaking off the excess oil, and spread the slices over the surface of the dough, either randomly or stacked like dominoes. If using Yukon Gold potatoes, you may need to overlap more tightly to fit on the dough. If using onions, scatter them over the potatoes. Place the sheet pan on the middle shelf of the oven, bake for 5 minutes, and then lower the temperature to 400°F (200°C). Bake for 15 minutes, then rotate the pan 180 degrees. Continue to bake for 20 to 25 minutes longer or until the dough and the potatoes are golden around the edges.
Remove the finished focaccia from the oven and immediately transfer it to a cooling rack. Drizzle any oil remaining in the pan, as well as any remaining herb oil, to taste, over the potatoes. Season with salt and pepper, then let cool for at least 20 minutes before cutting and serving.