Spread softened butter on both sides of each piece of sandwich bread.
Heat a skillet over medium heat and place two slices of bread in the skillet. Place a slice of each type of cheese on each piece of toast and top with basil leaves. Then close the sandwich with the other bread slice.
Cook the sandwich until both sides are golden brown and the cheese is melted. This should take about 5 minutes. Repeat with the other sandwich bread.
Remove the sandwiches from the skillet and transfer them to a cutting board. Cut the sandwiches in half (or quarters) and serve warm!