In a medium bowl, combine the shredded chicken, mashed avocado, Greek yogurt, lime juice, garlic powder, salt, and black pepper. Mix well until all ingredients are fully incorporated.
Preheat a skillet or griddle over medium heat.
Spread butter on one side of each slice of bread.
On the unbuttered side of two slices, spread a generous amount of the chicken and avocado mixture. Top with shredded cheddar cheese and sprinkle with chopped cilantro if using.
Place the other two slices of bread on top, buttered side facing out.
Place the sandwiches in the preheated skillet. Cook for 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove from the skillet, slice in half, and serve warm.