In a medium bowl, combine the shredded cheddar and mozzarella cheeses. Add the softened cream cheese and mix until well blended.
Stir in the chopped basil and honey, then season with salt and pepper to taste.
Spread a thin layer of the butter on the cut sides of each Hawaiian roll.
Place the bottom half of each roll in a skillet over medium heat.
Spoon an equal portion of the cheese mixture onto each roll's bottom half, then place the top halves of the rolls back on.
Grill the sandwiches in the skillet, pressing down gently with a spatula, for about 3-4 minutes until the bottoms are golden brown and the cheese begins to melt.
Carefully flip each sandwich and grill the other side for another 3-4 minutes, until golden brown and the cheese is fully melted.
Remove from the skillet, slice in half and serve warm.
Notes
Serve the grilled cheese sandwiches on a colorful platter, garnished with a sprig of basil and a drizzle of honey to add a gourmet touch.