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 down nearly to the bottom without slicing all the way through.
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 - Brush the garlic herb butter generously over each potato, taking care to work the mixture down between the sliced sections for even flavor distribution.
05 - Loosely wrap each potato in a double layer of aluminum foil, keeping the top slightly open to allow some crisping during grilling.
06 - Place the foil-wrapped potatoes directly on the grill grates, 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 develop a crispy exterior.
07 - Transfer the finished potatoes to a serving platter. Sprinkle with grated Parmesan cheese and chopped chives, and serve immediately while hot. Pass extra butter at the table if desired.