Put the eggs in a large pan and pour in cold water to cover. Heat the water, and then when it boils, reduce the heat and simmer the eggs for 10 minutes. Stir the eggs twice so they cook evenly.
Drain the eggs, hold them under cold water, and remove the shells. Dry the eggs and then chop them roughly.
Place the chopped eggs in a large bowl, then add the onions, season with salt and pepper; mix well to combine. Add enough mayonnaise to bind the mixture together, and then stir in the mustard, if using.
Sprinkle the chopped parsley on top to garnish. Serve immediately, or if you have time, chill before serving with rye toast and crackers.