Add enough water to a large pot to cover potatoes. Salt water using 1 tsp salt. Bring to a boil, then carefully add potatoes. Cook for 15-20 minutes, or until cooked through.
Drain potatoes. For the oven, preheat to 450 degrees. Place on a lined baking sheet. Using a fork (or your gloved hand) press down on potatoes to "smash." Drizzle with olive oil, seasoning and herbs, then roast for 15 minutes or until smashed areas of potatoes are beginning to crisp up. In last 5 minutes of cooking, sprinkle with parmesan. Remove and serve.
For the grill: Place drained potatoes in a bowl. Toss with olive oil, seasoning and herbs (if desired.) Place on a griddle and lightly smash. Cook for 5-7 minutes per side until browning and crisping. In the last 5 minutes of cooking, sprinkle parmesan over potatoes. Remove and serve.