In the work bowl of a food processor, pulse together cream cheese, dill, chives, parsley, cream, salt, and pepper until herbs are finely chopped and mixture is smooth.
Spread a thick even layer of cream cheese mixture onto 2 bread slices. Stack on top of each other, cream cheese side up. Top with a third bread slice to make a triple-stack sandwich. Repeat with remaining bread slices and cream cheese mixture to create a second triple-stack sandwich.
Using a long serrated bread knife in a gentle sawing motion, trim and discard crusts from sandwiches. Cut each sandwich into 3 finger sandwiches. Serve immediately, or cover with damp paper towels, place in a covered container, and refrigerate until serving time.
Recipe by TeaTime Magazine at https://teatimemagazine.com/herbed-cheese-triple-stack-sandwiches-recipe/