Jim Lahey, owner of the Sullivan Street Bakery in New York City, counts this traditional Italian pizza as one of his favorites.
Combine flour, 1/2 teaspoon salt, sugar, and yeast in the bowl of an electric mixer, and slowly add 1 3/4 cups cold water. Mix on low speed until ingredients begin to combine. Increase speed to medium high, and continue to mix for about 10 minutes until the dough is smooth and elastic and cleanly pulls away from the sides of the mixing bowl.
Place dough in an oiled bowl, and allow to rest for 2 to 4 hours until it has doubled in size.
While the dough rests, prepare the potato topping. Slice potatoes very thin using a knife or a mandoline. Then soak them in several changes of ice water to remove excess starch and prevent discoloration. Drain slices in a colander, toss with 1/2 teaspoon salt, and set aside for 10 minutes. Drain any accumulated water. In a medium bowl, combine potatoes, onions, and 1 tablespoon olive oil, and set aside.
Preheat oven to 440 degrees. Prepare two rimmed baking sheets with vegetable oil. Divide dough in half. Place each piece on its own baking sheet. Using the palms of your hands, flatten dough out to the edges of the pan. Evenly spread potatoes over the surface of the dough up to the very edge, or about 1 inch from the edge if you desire a crust on your pizza. Season with remaining 1/2 teaspoon salt and remaining 3 tablespoons olive oil.
Bake potato pizza until it has shrunk away from the edges of a pan and the bottom is golden brown, about 30 minutes. Remove from oven, and allow to cool slightly; slice into pieces, and serve. Potato pizza is also delicious served at room temperature.