In a mixing bowl, combine the shredded cooked chicken with basil pesto. Stir until well-coated.

Preheat a non-stick frying pan on low heat. Butter one side of each slice of bread.

Lay one slice of bread, butter-side down, in the skillet. Layer with mozzarella, chicken-pesto mixture, sun-dried tomatoes, and remaining mozzarella. Top with the second slice of bread, butter-side up.

Spread more butter on the top slice and press down gently. Cook for 3-5 minutes.

Flip the sandwich and cook for another 3-5 minutes until both sides are golden and cheese is melted.

Let the sandwich sit for a minute, then slice diagonally and serve warm.