1. Spread butter on 1 side of each slice of bread. Spread pesto on unbuttered side of bread. Top four slices with half the cheese (it won’t cover), followed by red pepper (cut to fit bread), arugula then remaining cheese. Top with second slice of bread, laying pesto side down, butter side out.
2. Heat a large non-stick skillet over medium heat. Place 2 to 4 sandwiches in pan depending on size, cooking until deep golden and cheese begins to melt, for 2 to 4 min. Flip and cook on the other side until deep golden and cheese is melted, for 2 to 4 min. Repeat, if needed, for other 2 sandwiches. Slice sandwiches in half.