Peel the eggs and roughly chop; set aside.

In a large bowl, whisk together the Greek yogurt, Dijon mustard, lemon zest, salt and pepper. Add the chopped eggs, celery and parsley, and stir to combine with the dressing.

Divide the egg salad mixture between 4 slices of bread. Add lettuce and close the sandwiches with the remaining bread. Slice in half if desired.