In a medium bowl, combine the shredded chicken and mashed avocado until well mixed.
Add the cheddar cheese, mayonnaise, lime juice, garlic powder, salt, and pepper to the chicken-avocado mixture. Stir until all ingredients are evenly incorporated.
Heat a non-stick skillet over medium heat and add 1 tablespoon of olive oil.
Place 2 slices of bread in the skillet, and spread half of the chicken-avocado mixture on each slice.
Top with the remaining two slices of bread and gently press down.
Cook for about 3-4 minutes on each side, or until the bread is golden brown and crispy, and the cheese is melted. Add the remaining olive oil to the skillet if needed.
Once cooked, remove from heat and let it sit for a minute before slicing.
Garnish with fresh cilantro or parsley before serving.