In a medium bowl, combine the chicken, mayonnaise, honey mustard, celery, parsley, hot sauce, and vinegar or pickle brine (if using).
Season with salt and pepper to taste, then stir well until everything is evenly mixed. Set aside or refrigerate briefly.
Now, lightly spread softened butter on one side of each bread slice.
On the unbuttered side of two bread slices, layer the sandwiches in this order: A slice of cheddar, a generous scoop of the chicken salad, a slice of gouda or pepper jack if using, 4 bacon slices, 2 tomato slices, pickled onions or pickles and red onion slices if using. Top with a second slice of bread, buttered side facing out.
Heat a nonstick skillet or griddle over medium heat: Add the sandwichs and cook until golden brown and the cheese has melted about 3-4 minutes per side. Using a spatula, press the sandwiches lightly to help the melt come together.