Place the potatoes and 1 tablespoon salt in a large saucepan and add enough water to cover the potatoes. Bring to a boil, reduce the heat, and simmer for 17 to 20 minutes, until the potatoes are tender when pierced with a skewer. Drain the potatoes and place on a sheet pan. With a potato masher or metal measuring cup, press each potato until it's about 1/2 inch thick (they will be messy). Toss the potatoes with the olive oil, 1 teaspoon salt, and 3/4 teaspoon pepper.
Roast the potatoes for 25 to 30 minutes, turning once, until the skins have become nicely browned. Sprinkle the potatoes with the Parmesan cheese and roast for another 2 to 3 minutes, just until the cheese melts. Sprinkle the potatoes with the chives and fleur de sel and serve hot.