Place a large skillet over medium heat and melt the butter. Place four slices of bread in the skillet and divide the mozzarella, roasted red peppers and Parmigiano-Reggiano between each of them. Top each with the second slice of bread and cook for another minute or until the bottom sliced is golden brown.
Carefully flip the panini and cook for another 1-2 minutes or until the cheese has melted and the other side is golden brown.
To serve, remove the panini from the heat and cut each of them into quarters. Garnish with chopped basil.