Add the chicken, apples, celery, shallot, cheddar, basil, and chives to a large bowl.
In a separate bowl, whisk together the mayonnaise, whole grain mustard, Dijon, apple cider vinegar, maple syrup, salt, and black pepper.
Pour the dressing over the chicken salad and toss until everything is evenly coated. Taste and adjust with more salt, pepper, maple syrup, or apple cider vinegar as needed.
To make the melt: Slice a croissant lengthwise, toast it and melt a slice of cheddar on it, then place the cold chicken salad inside. Eat it while the salad is cold and the croissant is warm.