Place the potatoes in a large pot and cover them with cold salted water. Bring to a boil over high heat. Once boiling, reduce the heat slightly and simmer for 15 to 20 minutes, or until the potatoes are fork-tender. Drain them thoroughly and let them sit for a few minutes to allow excess steam to escape.
Preheat your oven to 425°F (220°C). Lightly grease a large baking sheet with olive oil or line it with parchment paper for easy cleanup. Place the drained potatoes on the sheet, leaving enough space between them for smashing.
Use the bottom of a heavy glass, a potato masher, or a small jar to gently press down on each potato until it is about 1/2 inch thick. Try to keep the potato in one piece while creating plenty of craggy edges and flat surfaces for crisping.
In a small bowl, whisk together the olive oil and minced garlic. Brush this mixture generously over the top of each smashed potato. Sprinkle evenly with salt, pepper, and dried parsley.
Place the baking sheet in the oven and roast for 15 minutes. Remove the sheet from the oven and sprinkle the grated Parmesan cheese over the potatoes. Return to the oven for another 5 to 10 minutes, or until the cheese is melted and the edges of the potatoes are crispy and golden brown.
Remove from the oven and let them cool for a minute. Garnish with fresh parsley if desired and serve while hot for the best texture.