01 - Set your grill to medium-high heat, targeting approximately 400°F. Allow the grates to fully heat before placing any food.
02 - Wash and scrub each potato thoroughly under running water. Place each potato between two wooden spoons or chopsticks to act as a cutting guide, then slice crosswise at 1/8-inch intervals, cutting nearly through to the bottom without separating the base.
03 - In a small mixing bowl, combine the melted butter, minced garlic, chopped parsley, thyme leaves, kosher salt, and black pepper. Stir until evenly blended.
04 - Using a pastry brush, generously coat each potato with the garlic herb butter, taking care to work the mixture down between the accordion slices for even flavor distribution.
05 - Loosely wrap each potato in a double layer of aluminum foil, leaving the top partially open to allow the edges to crisp during grilling.
06 - Place the foil-wrapped potatoes directly on the grill grate, close the lid, and cook for 35 to 40 minutes. Brush with additional garlic butter every 10 to 12 minutes. Remove the foil for the final 5 to 10 minutes to achieve a golden, crisp exterior.
07 - Transfer the potatoes to a serving platter. Finish with grated Parmesan cheese, chopped chives, and a crack of fresh pepper. Serve immediately while hot.