In a mixing bowl, combine the shredded chicken with the mayonnaise, lime juice, garlic powder, salt, and black pepper. Mix until well combined.
In another bowl, mash the avocado and stir in the chopped cilantro if using. Season with a pinch of salt and mix until creamy.
Preheat a skillet over medium heat and add the olive oil.
Spread the chicken mixture evenly onto two slices of whole-grain bread. Top with the mashed avocado and sprinkle the shredded cheese over the top.
Place the remaining slices of bread on top to form sandwiches.
Once the skillet is hot, carefully place the sandwiches in the skillet. Cook for about 3-4 minutes on each side, or until the bread is golden brown and the cheese has melted.
Remove the sandwiches from the skillet and let them rest for a minute before slicing in half. Serve warm.