Heat the oven to 425°F. Put the potatoes in a large pot and cover with cold water by 1 inch. Add the salt, bring to a boil, and cook for 15 minutes, until a knife slides into the center with little resistance.
Drain the potatoes and let them steam-dry in the colander for 5 minutes.
Brush a rimmed sheet pan with 1 tbsp of the olive oil. Set the potatoes on the pan 2 inches apart and smash each one to about 1/2 inch thick with the bottom of a measuring cup.
Stir the grated garlic into the remaining 2 tbsp olive oil and drizzle it over the potatoes. Sprinkle with the Parmesan, rosemary and pepper.
Roast for 25 minutes, until the edges are deep golden and crisp. Add 5 minutes if you want them extra crunchy.
Scatter the parsley over the top and serve hot.
