With a push pin, pierce the large ends of eggs to release the air bubble, which otherwise can expand during cooking, cracking the egg shell. Into a 3-quart sauce pan place the eggs. Pour in 2 1/2 quarts of cold water. Bring just to the rolling boil, remove from heat, cover the pan closely, and set the timer for 17 minutes.
Transfer the eggs to a bowl of ice cubes and water, and let cool for 2 minutes (to shrink the egg body from the shell) while you bring the egg water back to the boil. Then transfer the eggs back into the boiling water and let boil for exactly 10 seconds (to expand the shell from the egg body).
At once, and 1 by 1, tap an egg gently all over on a hard surface to crack the shell and starting at the large end, peel under a thin stream of cold water. Return it to the iced water, and continue with the rest. Let them chill a good 20 minutes in the iced water?rapid cooling helps prevent the dark line between yolk and white.
Always store hard-boiled eggs in the refrigerator, submerged in ice water in an uncovered container, where they will keep perfectly 3 to 4 days.
Scrub the potatoes under running water with a vegetable brush, and place in a steamer basket over a saucepan containing 2 inches of water. Bring to the boil, lower heat to moderate, cover closely, and steam about 20 minutes or until cooked through?be sure they are really cooked through, cut one in half and taste carefully. Peel while still hot, halve them, cut into slices 1/4-inch thick.
In a 2-quart bowl, combine salt, shallots, wine, and water. Lift the potatoes gently into a the 2-quart bowl. Using a bulb baster, so as not to break the slices, baste the potatoes with the liquid. Taste for seasoning adding more salt, if needed, grinds of pepper, and several spoonfuls of the olive oil. Baste several times as the potatoes cool.
In a large kettle, set over moderately high heat, bring 6 quarts of water to the boil. Wash and drain the green beans, then snap off both ends. Add 2 tablespoons of salt to the boiling water and drop the beans into the kettle. Cover the kettle for a moment, just until it boils again. Uncover at once and boil slowly (moderate bubbles) for 3 to 4 minutes. The beans are done when just cooked through?taste one to be sure?just tender with the slightest crunch. Drain immediately. At once return the beans to the kettle and run cold water into it to cool the beans rapidly, adding a tray or two of ice cubes if you have them. When chilled, in 5 minutes or so, drain again, dry in a clean towel, and refrigerate in a covered bowl until ready to assemble salad.
Separate the lettuce leaves, wash, and spin dry. Shortly before serving so that all elements will remain at their freshest, toss the lettuce leaves in a large bowl with just enough dressing to coat them. Taste the potatoes, adding a little more seasoning if necessary. Halve the eggs. Toss the green beans with a spoonful of the dressing. Lightly salt the cut surfaces of the tomatoes and dribble over a little dressing. Open and drain the anchovies, separating them with a form. Drain the canned tuna, flake gently, and season with lemon juice and pepper. Arrange the largest lettuce leaves nicely around the sides of the serving bowl or platter, and make a bed of the remaining leaves in the center, where you will pile the potatoes. Place the egg yolks against the lower part of the potatoes, spoon a dollop of mayonnaise over each yolk, and decorate with crossed strips of anchovies and a sprinkling of capers. Divide the beans, tomatoes, and tuna into 6 portions, and place at strategic intervals around the potatoes.
Survey the platter, scattering black olives and tucking parsley springs wherever needed. Serve as soon as possible.
Oil and Lemon Dressing:
Grate the lemon peel into a screw-top jar, add the salt, several grinds of pepper, mustard, minced shallots, and 1 tablespoon lemon juice. Shake well to blend, then pour in the oil and shake vigorously again. Taste for seasoning, adding more lemon, salt and pepper if needed.