Hard boil and peel the eggs. Cover with cold water in a saucepan. Bring to a boil over medium heat. Turn the heat to low and simmer for exactly 8 minutes. Run under cold water and break off the shells. Put them in a bowl.
Peel and chop the onion. Chop the eggs in the bowl with a fork, cutting them into small pieces.
Add mayo, chopped onions, Dijon mustard, paprika, chopped parsley, salt and pepper to the eggs. Stir until every ingredient mixes well. Chill egg salad for at least 4 hours.
Use 2 slices of bread per sandwich. Put one large lettuce leave (or 2-3 smaller ones) on one of the slices. Add 4 tbsp egg salad per sandwich, cover with the other slice. Cut in half for a nice presentation.