In a small saucepan add the cut up potato and 3 cups of water. Bring the mixture to a boil and cook for about ten minutes or until the potato can easily be poked with a fork. Using a slotted spoon transfer the cooked potato to a small bowl and then measure out one cup of the hot potato water and set both aside to cool.

Once the potato had cooled enough to touch grate it on the largest holes of your box graters and set aside (this should be about one cup of grated potato that is lightly packed).

Add the cooked potato, 3 1/2 cups of flour, 2 tablespoons of olive oil, yeast, and salt to the bowl of a stand mixer. Using the dough hook mix on low speed. Slowly add the reserved potato water (that has cooled to 110 degrees) and mix until it starts to form a dough, about 2 minutes.

Increase the speed to medium low and continue to mix until a smooth and elastic dough is formed. The dough should start to pull away from the edges of the mixer bowl but still stick to the bottom. If after 4 minutes the dough is too sticky add the remaining flour as needed just a tablespoon or two at a time until the dough leaves the edges of the bowl.

After 8 minutes knead the dough by hand on a clean surface to form a smooth round bowl. Put the dough in a big lightly oiled bowl and let it rise, covered with plastic wrap until doubled, about an hour to an hour and a half.

Coat the bottom of an 18 by 13 inch rimmed baking sheet with 1/4 cup olive oil. Using wet hands (so the dough doesn't stick to you) gently push the dough evenly across the bottom of the pan until the whole pan is evenly filled with dough. Brush the top with another 1 tablespoon of olive oil and then cover with plastic wrap and let it rise until doubled, 45 to 75 minutes.

At the end of the final rising time heat the oven to 425 degrees. Remove the plastic wrap and with wet fingertips dimple the entire top of the dough. Drizzle the last tablespoon of oil over the top and sprinkle evenly with the Parmesan cheese. Bake until the bread is crisp, 20 to 25 minutes.

Once the bread has baked carefully transfer it to a wire rack to cool (don't keep it in the pan). Let it cool for 10 minutes. Serve warm or at room temperature.