Place the potatoes in a large saucepan and cover with water by at least 1 inch. Bring to a boil, then reduce heat to a simmer. Cover and cook until the potatoes are very tender, about 20 minutes. Drain well.

Meanwhile, preheat your oven to 450°F (230°C). Line a 15x10x1-inch baking sheet with foil and brush it with 1 tablespoon of olive oil.

Transfer the cooked potatoes to the prepared pan. Using the bottom of a wide glass, gently press each potato down until about ½-inch thick, keeping the potato mostly in one piece.

Brush the smashed potatoes with the remaining tablespoon of olive oil. Season with ¼ teaspoon salt and ¼ teaspoon pepper.

Roast the potatoes uncovered for about 15 minutes, or until the bottoms start to turn golden and crisp.

Flip each potato carefully, sprinkle with the remaining ¼ teaspoon salt and ¼ teaspoon pepper, and continue roasting for another 10 to 15 minutes until golden and crispy all over.

Switch your oven to the broiler setting and position the rack 4 to 5 inches from the heat source. Sprinkle the Parmesan cheese evenly over the potatoes.

Broil for about 3 minutes, or until the cheese is melted, bubbly, and golden brown.

Remove from oven, garnish with minced parsley, and serve immediately.