Season the chicken breasts with salt and pepper on both sides.
Heat olive oil in a skillet over medium-high heat.
Cook chicken breasts for 6-7 minutes on each side until fully cooked.
Remove chicken and let rest before slicing thinly.
Slice the avocado and prepare the cheese slices.
Spread mayonnaise and Dijon mustard on each slice of bread.
Assemble sandwiches by layering sliced chicken, avocado, cheese, red onion, and tomato on two bread slices.
Top sandwiches with remaining bread slices, mayo side down.
Heat a skillet or grill pan over medium heat and add butter or olive oil.
Grill sandwiches for 3-4 minutes per side until bread is golden and cheese melts, pressing gently with a spatula.
Remove sandwiches and let cool for a minute before slicing in half.
Serve warm.