In a small bowl, mix the softened butter, mayonnaise, garlic powder, and dried oregano until well combined. If you like a hint of sweetness, stir in the honey.
Cut the Hawaiian rolls in half horizontally, keeping them connected.
Spread the butter mixture generously on the cut sides of each roll.
Layer the cheddar and gouda cheese between the bottom halves of the rolls.
Place the top halves of the rolls on the cheese and gently press down.
On the grill, place the assembled sliders and cook for about 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove the sliders from the grill and let them cool slightly.
Sprinkle with a pinch of sea salt and garnish with fresh basil leaves before serving.