01 - Combine mayonnaise and Dijon mustard in a small bowl, mixing until fully incorporated.
02 - Lay out all bread slices and spread the mayonnaise-mustard mixture evenly on one side of each slice.
03 - On half the bread slices (spread-side up), arrange shredded chicken, followed by avocado slices, tomato slices, red onion if using, and cheese slices. Season with salt and pepper to taste.
04 - Top each prepared slice with a remaining bread slice, spread-side facing down, to form complete sandwiches.
05 - Place a large skillet or grill pan over medium heat and add 1 tablespoon butter, allowing it to melt and coat the surface.
06 - Arrange sandwiches in the pan, working in batches if necessary. Press gently with a spatula and cook for 3-4 minutes per side, adding additional butter as needed, until bread achieves golden-brown color and cheese is fully melted.
07 - Transfer sandwiches from pan and let rest for 1 minute before slicing diagonally. Serve immediately while warm.