Arrange potato slices, separated by onion and butter slices, on a large piece of aluminum foil. Top with garlic, and season with parsley, salt, and pepper. Tightly seal potatoes in the foil.
Place on the preheated grill, and cook 20 minutes, turning once, or until potatoes are tender.
Sprinkle potatoes with Cheddar cheese, reseal foil packets, and continue cooking 5 minutes, until cheese is melted.
