Step 1

In a medium saucepan, combine the potatoes, herb sprigs, garlic, 1 teaspoon salt and 3 cups water. Cover and bring to a boil over high. Uncover, reduce to medium and simmer until a skewer inserted into the potatoes meets no resistance, 12 to 14 minutes. Drain, reserving the cooking liquid; let the liquid cool until just barely warm, 20 to 30 minutes (it should be no hotter than 115°F). Meanwhile, discard the herb sprigs, then return the potatoes, garlic and any loose herb leaves to the saucepan. Using a potato masher or fork, mash until smooth and creamy. Transfer the potatoes to the bowl of a stand mixer fitted with the dough hook.

Step 2

To the mixer bowl, add the flour, 2 tablespoons oil, the yeast, sugar and remaining ¾ teaspoon salt. Add 1¼ cups of the cooled reserved cooking water, then mix on low until the ingredients form a dough, about 1 minute.Increase to medium-high and mix until the dough clears the sides of the bowl but sticks to the bottom, 3 to 5 minutes, adding more cooking liquid 1 tablespoon at a time as needed (the dough should be very soft and sticky and just clear the sides of the bowl). Using a silicone spatula, scrape the sides of the bowl and gather the dough in the center. Cover with plastic wrap and let rise at room temperature until not quite doubled, 30 to 60 minutes. Meanwhile, coat the bottom and sides of a 9-by-13-inch metal baking pan with the remaining 2 tablespoons oil.

Step 3

Transfer the dough to the prepared pan and, using oiled fingers, press and spread it into an even layer, all the way into the corners. Cover and let rise at room temperature until puffed, 30 to 60 minutes. Meanwhile, heat the oven to 400°F with a rack in the middle position.

Step 4

When the dough is risen, use a chopstick to poke the dough all over, then sprinkle with the chopped herbs, olives (if using), Parmesan (if using) and a few grinds of black pepper. Bake until the edges are browned and crisp and the top is golden brown, 35 to 40 minutes. Cool in the pan on a wire rack for 10 minutes, then transfer the focaccia directly to the rack. Serve warm or at room temperature.