Preheat the oven to 425°F. Place the potatoes in a pot and cover with water. Bring to a boil and cook until fork-tender, about 15 minutes, then drain. Coat a baking sheet with 1 tablespoon of oil and set aside.

Use tongs to transfer the very hot potatoes to the oiled baking sheet. Use the back of a heavy measuring cup to smash each potato to about ¼ inch thick.

Drizzle the potatoes generously with the remaining oil and melted butter. Sprinkle with salt, garlic, and pepper. Sprinkle with about a teaspoon of parsley.

Roast for 30 minutes, until browned and crispy on the edges. Remove from the oven, and top with Parmesan cheese. Roast for an additional 5 minutes to melt the cheese.

Remove from the oven and sprinkle generously with parsley. Serve warm.