In a medium bowl, combine the shredded cooked chicken, mayonnaise, Dijon mustard, chopped celery, chopped red onion, chopped parsley, salt, and black pepper. Mix well until all ingredients are evenly incorporated to create the chicken salad.
Preheat a skillet or griddle over medium heat.
Lightly butter one side of each bread slice with the softened unsalted butter.
Place two slices of bread, buttered side down, on the skillet. Toast until golden brown, about 3-4 minutes.
Flip the bread slices and toast the other side for another 2-3 minutes until golden and crisp. Remove from heat.
On one toasted bread slice, layer one large lettuce leaf, two slices of tomato, half of the chicken salad mixture, two slices of turkey breast, and two slices of turkey bacon.
Place a second toasted bread slice on top, buttered side up.
Repeat the layering on the second sandwich with the remaining ingredients: lettuce leaf, tomato slices, chicken salad, turkey breast, turkey bacon, and top with the last bread slice.
Cut each sandwich diagonally into quarters and secure each quarter with a toothpick if desired.
Serve immediately while the bread is warm and crispy.