Prepare the Spread: In a small bowl, mix the mayonnaise and Dijon mustard (if using) until well combined.
Assemble Sandwiches: Spread the mayo mixture on each slice of bread. Layer with chicken, avocado slices, a slice of cheese, and optional lettuce or tomato. Top with the remaining slice of bread.
Grill the Sandwich: Heat a skillet over medium heat. Spread a thin layer of butter on the outer sides of each sandwich. Grill the sandwiches until golden brown and crispy, about 3-4 minutes per side, or until the cheese is melted.
Serve: Slice the sandwiches in half and serve warm. Enjoy your delicious, melty Chicken Avocado Sandwich!