In a large bowl, mix together the drained tuna, Greek yogurt, mayonnaise, red onion, celery, apple, parsley, dill, Dijon mustard, lemon juice, salt, and pepper.
Toast the slices of bread and spread butter on one side of each slice.
Spoon the tuna salad mixture onto two slices of the bread, spreading it evenly.
Top each sandwich with the remaining slices of bread, buttered side facing out.