Chopped fresh herbs such as parsleyrosemary, or basil, optional for serving
Rinse and dry the potatoes (no need to peel). Cut crosswise into ½-inch slices (if your potatoes are smaller than a golf ball, you can halve or quarter them). Place in a large bowl.
In a small bowl, stir together the rosemary, garlic powder, salt, pepper, and oregano.
Drizzle the potatoes with the oil, then sprinkle the spices over the top. Toss to evenly coat.
Preheat the grill to medium-high (about 375 to 400 degrees F).
Place two large (about 22 to 24 inches long) sheets of heavy-duty foil down on a large baking sheet (you'll use the baking sheet for easy transport) so that the foil pieces are slightly overlapping down the center to create a wider sheet. Coat with non-stick spray. Spread the potatoes onto the foil in a single layer (if you prefer not to have the food touch the foil, you can add a layer of parchment in between). Place two more overlapping sheets of foil on top, then fold up the edges all the way around to seal and create a packet. Leave some space towards the top of the packet to allow the air to circulate.
Using the baking sheet, carry the potatoes out to the grill, then with tongs slide the packet onto the grill. Cover then cook for 15 minutes.
Carefully open the foil then use the tongs to flip the potatoes over. They should be deeply golden on the first side (if not, continue to cook them for 3 to 5 minutes more). Place the foil loosely back over the top, close the grill, and cook for 5 to 10 additional minutes, until the potatoes are tender when pieced with a fork.
Slide the potato packet back onto the baking sheet, then transfer them to a serving bowl (or serve them right off of the foil). Serve warm, with a sprinkle of Parmesan and chopped fresh herbs as desired.
TO GRILL IN THE OVEN. Preheat your oven to 400 degrees F. Cook the potatoes directly on the oven rack for 20 minutes. Slide the packet onto a baking sheet and remove them from the oven. Carefully open the foil packet, flip the slices over, then slide the sheet back into the oven (leave the foil open). Continue cooking until the potatoes are golden and tender, about 10 to 15 minutes minutes more.
TO STORE. Refrigerate leftover grilled potatoes for up to 5 days.
TO REHEAT. Reheat in the oven at 350 degrees F, until heated through.
TO FREEZE. I do not recommend freezing potatoes, as their texture can become mealy once thawed.