Preheat the oven to 425°F. Lightly oil a rimmed baking sheet or spray it with nonstick cooking spray (you can line it with foil first, for easier clean up).
Place the potatoes in a pot and add water to cover. Salt the water, cover the pot, and bring to a boil over high heat. Reduce the heat and simmer for 15 to 20 minutes, until the potatoes are quite tender.
Drain the potatoes let them dry and cool for 5 minutes or so in the colander. Transfer them to the baking sheet. Use a sturdy metal spatula or the bottom of a can of beans or tomatoes, or anything else that seems appropriate, to press down on each potato, smashing it to about ½-inch thickness (they will burst open a bit, which is perfect).
Drizzle half of the olive oil over the potatoes, then flip the potatoes with your fingers or a spatula, and drizzle over the rest of the oil. Sprinkle them with salt. Bake for about 20 minutes, until they are crispy on the outside, but still nice and tender inside. Sprinkle the Parmesan (if desired) over for the last few minutes of cooking. Serve hot or warm.
Notes
If you want, you can put the smashed un-baked potatoes into a container and refrigerate them for up to a day before proceeding with the rest of the recipe (obviously don’t preheat the oven if this is your intention).