01 - Whisk together mayonnaise and Dijon mustard in a small bowl until smooth and fully combined.
02 - Lay out all bread slices. Generously spread the mayo-mustard mixture on one side of each slice.
03 - Layer half the bread slices with shredded chicken, followed by avocado slices, tomato, red onion, and cheese. Season with salt and pepper to taste.
04 - Top each sandwich with 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 surface.
06 - Place sandwiches in the pan, working in batches if necessary. Cook for 3-4 minutes per side, pressing lightly with spatula, until bread turns golden brown and cheese melts completely. Add more butter between batches if needed.
07 - Transfer sandwiches to a cutting board. Let rest for 1 minute, then slice diagonally and serve immediately while warm.