Heat a large non-stick skillet over medium-low heat. Melt half of the butter in the skillet. Place two sandwiches at a time in the skillet and brown for 2 minutes on each side, flipping them over with a spatula. Keep the sandwiches warm on a baking sheet in an oven preheated to 200°F (95°C) while you cook the remaining sandwiches in the remaining butter, or serve them as you go. Serve with maple syrup.