In a bowl, combine the shredded chicken and buffalo sauce, mixing well to coat the chicken evenly.
Heat a skillet over medium heat and add 1 tablespoon of butter, allowing it to melt.
Place one slice of bread in the skillet. Layer half of the cheddar cheese, followed by the buffalo chicken mixture, then the mozzarella cheese, and top with the second slice of bread.
Cook for about 3-4 minutes, or until the bottom slice is golden brown. Carefully flip the sandwich, adding the remaining tablespoon of butter to the skillet if needed.
Cook the other side for another 3-4 minutes, until golden brown and the cheese is melted.
Remove from the skillet, slice in half, and serve with blue cheese dressing and chopped green onions if desired.