01 - In a small bowl, whisk together mayonnaise and Dijon mustard until well combined.
02 - Lay out all bread slices. Generously spread the mayo-mustard mixture on one side of each slice.
03 - On four prepared bread slices, layer shredded chicken, avocado slices, tomato slices, red onion if using, and cheese slices. Season with salt and pepper to taste.
04 - Top each sandwich with the remaining bread slices, spread-side down, pressing gently to adhere.
05 - Heat a large skillet or grill pan over medium heat. Add 1 tablespoon butter and allow to melt and coat the pan.
06 - Place sandwiches in the pan, working in batches if necessary. Cook for 3-4 minutes per side, pressing lightly with a spatula, until bread is golden brown and cheese is fully melted. Add additional butter as needed between batches.
07 - Transfer sandwiches to a cutting board and let rest for 1 minute. Slice diagonally and serve immediately while warm.