1/2 to 2/3 cup shredded Parmigiano-Reggiano, 2 handfuls
Put the potatoes in a medium pot in a single layer. Pour in enough stock to come 1/4-inch up the sides of potatoes, and add the extra-virgin olive oil. Cover, bring to a boil, reduce heat to simmer and steam for 10 minutes. Remove the lid, raise the heat and reduce the stock. When the stock evaporates, squish potatoes to flatten them a bit with a masher. Crisp the potatoes a few minutes on each side, then season with black pepper. Stir in the butter and cheese and toss.