Follow the steps in order for the best result.
Prepare your grill by heating either a gas or charcoal grill to medium heat. If using charcoal, allow the coals to burn down to a medium heat, creating an even cooking surface.
Create a large foil packet using a sheet of heavy-duty aluminum foil, approximately 18x12 inches in size. Place the quartered potatoes and sliced carrots in the center of the foil.
Evenly distribute the butter over the vegetables, then sprinkle with seasoning salt and the grated Parmesan cheese.
Tightly seal the foil packet, ensuring there are no openings for steam to escape during cooking. This will help steam the vegetables to tenderness.
Place the foil packet directly on the grill grates over medium heat. Cook for 45-50 minutes, or until the potatoes and carrots are tender when pierced with a fork.
Carefully open the foil packet, allowing the steam to escape away from your face and hands. This will prevent burns from the hot steam.
Sprinkle the cooked vegetables with freshly chopped chives for added flavor and visual appeal. Serve immediately as a delicious side dish.