Mix the chicken, hot sauce, mayonnaise, carrot and green onion in a small bowl.
Butter the outside of each slice of bread. Mix the mozzarella cheese and cheddar cheese. Sprinkle a layer of the cheeses on the inside of one slice of bread.
Then top with the chicken mixture.
Sprinkle a layer of cheese over the chicken mixture.
Top with the other slice of bread (butter side up).
Heat a non-stick pan over medium heat. Place the sandwich on the hot pan. Grill until golden brown and the cheese has melted, about 2-3 minutes per side.
Then use a metal spatula to turn the sandwich over to its other side. Press down on the sandwich with the spatula.
The sandwich is done when the sides are toasted and the cheese is melted. Cut in half and serve.