Begin by rinsing and drying the new potatoes. If larger than a golf ball, slice into ½-inch pieces; otherwise, halve or quarter smaller ones.
Combine the rosemary, garlic powder, kosher salt, black pepper, and oregano in a small bowl.
In a large bowl, toss the potatoes with olive oil and the seasoning blend to coat evenly.
Preheat the grill to medium-high heat, about 375 to 400 degrees Fahrenheit.
Arrange two large, overlapping sheets of heavy-duty foil on a baking sheet and coat with non-stick spray.
Spread the potatoes in a single layer on the foil. Cover with more overlapping foil sheets, sealing the edges completely but leaving space inside for air circulation.
Transfer the packet to the grill using the baking sheet, then cover and cook for 15 minutes.
Carefully open the foil, flip the potatoes with tongs; if not golden yet, cook 3 to 5 minutes more on the first side before flipping.
Cover loosely with foil and continue cooking for another 5 to 10 minutes, until the potatoes are tender when pierced.
Transfer grilled potatoes to a serving bowl, top with Parmesan and fresh herbs if desired, and serve warm.