Cut your potatoes into 1-inch chunks, aiming for uniform size so they cook evenly on the grill. While prepping the potatoes, mince your garlic cloves fresh—you'll notice the aroma is much more vibrant than pre-minced garlic. In a large bowl, combine the olive oil, minced garlic, Italian seasoning, smoked paprika, red pepper flakes, salt, and pepper. Whisk together until well combined, creating an aromatic seasoning oil.
Add the cut potatoes to the bowl with the seasoning mixture and toss thoroughly until every piece is evenly coated. Tear out sheets of heavy-duty aluminum foil and divide the seasoned potatoes between them, distributing them in a single layer on each sheet. Fold the foil up and over the potatoes, sealing the edges tightly to create closed packets—this traps the steam and heat for even cooking.
Heat your grill to medium-high heat (around 400°F if you have a thermometer). Once hot, place the sealed foil packets directly on the grill grates. Cook for 10-12 minutes, then carefully flip each packet using tongs—I like to use a thick dish towel to protect my hands when handling the hot foil. Continue grilling for another 10-12 minutes until the potatoes are tender when pierced with a fork.
Carefully open the foil packets by folding back the edges (watch for the steam!). Immediately sprinkle the Parmesan cheese and fresh chopped parsley over the hot potatoes while they're still steaming—this helps the cheese melt slightly and the herbs release their fragrance. Serve directly from the foil packets for a rustic presentation.