In a medium bowl, stir together shredded chicken and buffalo sauce until fully coated.
Butter one side of each slice of bread. On two of the slices, buttered side down, layer the Monterey Jack cheese, a few spoonfuls of shredded buffalo chicken, and the blue cheese crumbles. Top with the remaining two slices of bread, buttered side up.
Cook sandwiches on a skillet or griddle over medium heat until bread is golden brown and toasted, about 3-4 minutes. Reduce heat to medium-low and flip to cook the other side, 2-3 minutes or until bread is golden brown and the cheese has melted.
Serve and enjoy!