In a medium bowl, combine the shredded chicken, buffalo sauce, and softened cream cheese. Toss until the chicken is evenly coated. Stir in chives if using.

In a separate small bowl, toss the grated sharp cheddar and Monterey Jack cheeses together.

Spread softened butter or mayonnaise evenly over one side of each slice of bread, reaching all the way to the edges.

Heat a large non-stick skillet or cast-iron pan over medium-low heat.

Place two slices of bread into the skillet, buttered-side down. Top each slice with a handful of the mixed cheese.

Spoon the buffalo chicken mixture evenly over the melting cheese. Top with the remaining cheese mixture.

Place the remaining slices of bread on top, buttered-side facing up.

Cook for 4-6 minutes until the bottom bread is deeply golden and crispy. Carefully flip the sandwiches.

Cook for another 4-5 minutes on the other side until golden brown and the cheese is completely melted.

Remove from skillet, let rest for 1 minute, slice, and serve hot.