Add the softened cream cheese, crumbled blue cheese, paprika, black pepper, and optional cayenne to a small mixing bowl.
Mash and stir until the ingredients form a creamy, evenly seasoned mixture. Set aside.
In a separate bowl, combine the shredded cooked chicken, buffalo-style hot sauce, ranch dressing, and minced garlic.
Stir thoroughly until every piece of chicken is coated in the creamy buffalo sauce.
Arrange the bread slices on a clean work surface.
Spread softened butter over one side of each slice. These buttered surfaces will become the outsides of the sandwiches.
Turn four bread slices over and spread the cream cheese and blue cheese mixture over their unbuttered sides.
Divide the buffalo chicken mixture evenly among the four sandwiches, using approximately ½ cup per sandwich.
Place 1–2 slices of Muenster cheese over the chicken, depending on how cheesy you want your sandwiches.
Top with the remaining bread slices, keeping the buttered sides facing outward.
Heat a large skillet or griddle over low to medium-low heat. Add the Buffalo Chicken Grilled Cheese sandwiches without overcrowding the pan.
Cook for approximately 4–5 minutes on the first side, or until deeply golden and crisp.
Carefully flip each sandwich and cook for another 4–5 minutes, until the second side is golden and the cheese inside has completely melted.
If necessary, cook the sandwiches in batches so each one has enough contact with the skillet.
Transfer to a cutting board and allow them to rest for 1–2 minutes before slicing.
Serve warm with extra buffalo sauce or halal-friendly ranch dressing if desired.