Preheat oven to 425°F (220°C) with a large rimmed aluminum baking sheet inside for 5 minutes.
Stir together the softened butter, mayonnaise, garlic powder, and parsley. Spread evenly onto one side of all 12 bread slices.
Place 6 bread slices buttered-side down on the baking sheet. Layer with sliced Gruyère and shredded sharp cheddar, then top with the remaining 6 bread slices, buttered-side up.
Bake for 6 minutes until golden on the bottom, flip each sandwich, and bake for 4-5 minutes more until both sides are crisp and cheese is melted.