Start by making the dressing, to do this dissolve the salt in the lemon juice and vinegar for 30 minutes, then shake it with the rest of the ingredients in a screw-top jar to get everything thoroughly amalgamated.
Put the eggs in a saucepan, cover them with cold water, bring them up to a gentle simmer and cook gently for exactly 7 minutes. Then cool them rapidly under cold running water until they're quite cold.
Now take the shells off and chop the eggs roughly, seasoning them with a little salt and pepper. Then slice the potatoes into rounds and cut the beans into 1 inch (2.5cm) lengths.
Now take a large bowl, carefully mix the chopped eggs, beans and potatoes together, and pour in nearly all the vinaigrette dressing, keeping a little for later.
Stir again, to get everything coated with the dressing, then cover the mixture and chill it until needed.
To serve the salad, arrange the lettuce leaves in a salad bowl and sprinkle them with the reserved dressing; then arrange the potato mixture over the lettuce, make a criss-cross pattern with the anchovies and finally sprinkle on the black olives.