In a mixing bowl, thoroughly combine the shredded sharp cheddar and mozzarella cheeses. Add the softened cream cheese and blend until the mixture is smooth and homogeneous.
Mix in the finely chopped basil and honey, ensuring an even distribution, then season the mixture with salt and freshly ground black pepper according to your taste preferences.
Take the halved Hawaiian rolls and spread a thin, even layer of softened butter on the cut sides of each half, ensuring good coverage for flavor.
Heat a skillet over medium heat and carefully place the bottom halves of the rolls in the skillet, cut side up.
Generously spoon the cheese mixture onto each bottom half of the rolls, distributing it evenly. Cap each one with its top half to form a complete sandwich.
Grill the sandwiches in the skillet, pressing down lightly with a spatula for about 3-4 minutes. Keep an eye out for the bottoms to become golden brown, and for the cheese to start melting.
Using a spatula, gently flip each sandwich over and grill the other side for an additional 3-4 minutes, until it is also golden brown and the cheese is fully melted.
Once cooked, remove the sandwiches from the skillet. Slice them in half diagonally for a visually appealing finish and serve warm.
Notes
Arrange the grilled cheese sandwiches on a vibrant platter, garnishing each with a sprig of fresh basil and a drizzle of honey for a gourmet touch.