from America's Test Kitchen
1 russet potato (8 ounces), peeled and cut into 1-inch chunks
3 1/2 cups all-purpose flour
1 1/2 tsp yeast
1 1/4 tsp table salt
1 cup warm water
1/4 cup extra-virgin olive oil, plus extra for the baking sheet
3/4 tsp coarse sea salt or 1 1/4 tsp kosher salt
Cover the potato with water in a small saucepan and simmer until completely cooked and easily pierced with a knife, 10 to 15 minutes. Drain and when the potato is cool enough to handle, grate it on the large holes on the grater. Reserve 1 1/3 cups lightly packed potato.
Mix 3 1/4 cups of the flour, yeast, and table salt together in a standing mixer fitted with the dough hook. With the mixer on low speed, add the grated potato, water, and 2 Tbsp of the oil until the dough comes together, about 1 minute.
Increase the speed to medium-low and knead until the dough is smooth and elastic, about 10 minutes. (If, after 5 minutes, more flour is needed, add the remaining 1/4 cup flour, 1 Tbsp at a time, until the dough clears the side of the bowl but sticks to the bottom.
Turn the dough out onto a clean counter and knead by hand to form a smooth, round ball, about 1 minute. Place the dough in a lightly oiled bowl and wrap tightly in lastic wrap. Let rise in a warm place until doubled in size, 1 to 1 1/2 hours.
Press the dough into a well-oiled 12 by 18 inch rimmed baking sheet. Wrap loosely in lightly greased plastic wrap and let rise in a warm place until it has nearly doubled in size and springs back slowly when indented with a finger, 45 to 60 minutes.
Adjust an oven rack to the lower-middle position and heat the oven to 425 degrees. Wet your fingers and press them into the dough at regular intervals to make about 24 dimples. Drizzle with the ramining 2 Tbsp oil and sprinkle evenly with Parmesan and sea salt. Bake util the focaccia bottom is golden and crisp, 20 to 25 minutes.
Slide the focaccia onto a wire rack and let cool slightly before cutting into squares.