01 - Preheat grill to medium-high heat, approximately 400°F. Ensure grates are clean and lightly oiled.
02 - Wash and scrub potatoes thoroughly under running water. Place each potato between two wooden spoons or chopsticks to act as a cutting guide. Slice crosswise at 1/8-inch intervals, cutting nearly through to the bottom without separating the potato.
03 - In a small mixing bowl, combine melted butter, minced garlic, chopped parsley, thyme leaves, kosher salt, and black pepper. Stir until well blended.
04 - Brush the garlic herb butter generously over each potato, carefully working it between the accordion slices for even flavor distribution.
05 - Wrap each potato loosely in a double layer of aluminum foil, leaving the top slightly open to allow crisping during grilling.
06 - Place foil-wrapped potatoes directly on the grill, cover, and cook for 35 to 40 minutes. Brush with additional garlic butter every 10 to 15 minutes. Remove the foil for the final 5 to 10 minutes to develop a crisp, golden exterior.
07 - Transfer potatoes to a serving platter. Sprinkle with grated Parmesan cheese and chopped chives. Add fresh cracked pepper to taste and serve immediately while hot.