01 - Combine mayonnaise and Dijon mustard in a small bowl, mixing until smooth and evenly blended.
02 - Lay out all bread slices and spread the mayo-mustard mixture evenly on one side of each slice.
03 - On four bread slices (spread-side up), layer cooked chicken, avocado slices, tomato slices, red onion if desired, and cheese slices. Season generously with salt and freshly ground black pepper.
04 - Top each assembled sandwich with a remaining bread slice, spread-side down, pressing gently to adhere the layers together.
05 - Place a large skillet or grill pan over medium heat. Add 1 tablespoon of unsalted butter and allow it to melt completely, coating the pan surface.
06 - Transfer sandwiches to the hot pan, working in batches if necessary. Press lightly with a spatula and cook for 3 to 4 minutes per side, adding additional butter as needed, until bread achieves golden brown color and cheese melts completely.
07 - Remove sandwiches from pan and let rest for 1 minute before slicing diagonally. Serve warm while cheese remains melted and gooey.