Step 1Chop the eggs. Stir in the onion, celery, mustard, vinegar, mayonnaise and salt. Cover and chill until ready to serve.
Step 2Toss together the shredded lettuce and dill.
Step 3Divide the egg salad among 4 slices of the bread, spreading it to the corners. Grind black pepper over the egg salad, then place equal amounts of the lettuce-dill mixture on each sandwich. Top with the remaining bread slices. Cut in half and serve.