In a medium bowl, combine the shredded chicken, mashed avocado, mayonnaise, garlic powder, onion powder, salt, and pepper. Mix well until all ingredients are evenly combined.
Heat a skillet over medium heat and add the olive oil or butter.
Spread a generous amount of the chicken and avocado mixture onto two slices of bread. Top each with a quarter cup of shredded cheddar cheese. If desired, add fresh lettuce and tomato slices.
Place the remaining slices of bread on top to form sandwiches.
Carefully place the sandwiches in the heated skillet. Cook for about 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.