Step 1

In a large bowl, whisk together the water and salt until the salt is completely dissolved.

Step 2

Use a mandoline slicer or the slicing side of a box grater to slice the potatoes paper thin. Place the sliced potatoes in the bowl of salted water and press them down so they are fully submerged. Set aside to soak for 30 minutes to 1 hour.

Step 3

Preheat the oven to 500°F. If you're using a baking stone/steel, place the stone/steel in the bottom third of the oven before you start preheating.

Step 4

When the potatoes are done soaking, drain them in a colander and pat them dry with paper towels or a clean kitchen towel.

Step 5

Place the potato slices in a large bowl. Add the 2 tablespoons of olive oil, the minced onion, a few grinds of black pepper, a large pinch of salt, and the chopped rosemary. Use your hands to gently toss everything together until the potatoes are evenly coated and the seasonings and onion are evenly distributed.

Step 6

Stretch or roll out the pizza dough to a 12- to 14-inch round (or a 10-by-14-inch rectangle, for a classic Roman-style pizza). Transfer the dough to an oiled baking sheet or a lightly floured pizza peel (if using a baking stone/steel).

Step 7

Spread the potatoes in an even layer on top of the dough, making sure the potato slices go all the way to the edges of the dough. Sprinkle with another pinch or two of salt and a grind or two of black pepper.

Step 8

Transfer the pizza to the oven and bake for 10 to 15 minutes, until the bottom of the crust is evenly browned and the potatoes are tender and beginning to brown in spots.

Step 9

Remove the pizza from the oven. Drizzle with olive oil, season with a pinch of salt, and scatter on the whole rosemary leaves. Finish with the finely shredded Parmigiano-Reggiano cheese, if using. Slice and serve.