Season both sides of the chicken breasts with salt and pepper. Heat olive oil in a skillet over medium heat. Cook chicken for 6–7 minutes per side until cooked through and no longer pink. Let rest before slicing.

While the chicken rests, slice avocado and cheese. Dice red onion and slice tomato, arranging all on a plate for assembly.

Spread mayonnaise on one side of each bread slice, then add Dijon mustard. Layer chicken, avocado, cheese, red onion, and tomato on two slices. Top with remaining bread slices, mayo side down.

In the skillet, add butter or olive oil. Grill sandwiches for 3–4 minutes per side until golden brown and cheese melts.

Remove sandwiches from skillet, let cool for a minute, then slice in half. Serve warm with a light salad or chips.