In a mixing bowl, combine the shredded chicken, mashed avocado, lime juice, garlic powder, salt, and pepper. Mix well until all ingredients are fully blended.
Preheat a large skillet or grill pan over medium heat. Brush one side of each slice of bread with olive oil.
Place two slices of bread in the skillet oil-side down.
Spread an even layer of the chicken and avocado mixture over the bread slices in the skillet.
Sprinkle shredded mozzarella cheese evenly over the mixture, followed by halved cherry tomatoes and chopped red onion.
Top each with another slice of bread, oil-side up, creating a sandwich.
Cook for about 4-5 minutes until the bottom is golden brown and crispy. Carefully flip the sandwiches and cook for an additional 4-5 minutes on the other side, until the cheese is melted and the bread is golden.
Remove from heat and allow to cool slightly before cutting in half.