In the work bowl of a food processor, pulse chicken until finely chopped.
In a medium bowl, stir together chicken, cream, apple, mustard, celery, salt, and pepper until well combined. Spread an even layer of chicken salad onto 8 bread slices. Cover with remaining bread slices.
Using a serrated bread knife in a sawing motion, cut and discard crusts from sandwiches. Cut each sandwich into 3 equal rectangles, creating 3 finger sandwiches. Serve immediately, or cover with damp paper towels, place in a covered container, and refrigerate until serving time.
Notes
Make-Ahead Tip: Chicken salad can be made a day in advance and stored in a covered container in the refrigerator.
Recipe by TeaTime Magazine at https://teatimemagazine.com/green-apple-chicken-salad-sandwiches-recipe/