To prepare the sauce: With a spoon, pound together the garlic and salt to a paste. Beat in a T each of lemon juice and wine vinegar and the dry mustard. Slowly whisk in the olive oil and the pepper and basil. Refrigerate until ready to use.
To prepare the potatoes: Scrub the potatoes; steam or boil unil tender, about 20 minutes. Cut into chunks, or slice 1/2 inch thick. Toss potatoes gently with shallots, salt, pepper, chicken broth and water. Allow to sit 4 minutes, tossing once or twice to absorb liquid evenly. Add 1/4 cup dressing, toss again and refrigerate.
To prepare the salad: Place the beans in boiling water 5 minutes. Drain and rinse with cold water until chilles. Drain and pat dry; chill.
Toss the lettace with several spoonfuls of dressing and arrange the leaves around the edge of a large, deep platter. Turn the potato salad into the middle of the leaves. Arrange tomatoes around the potatoes and drizzle with a little dressing. Toss the beans with a spoonful of dressing and arrange around tomatoes.
Distribute the eggs and garnish with anchovies and capers. Ring the potatoes with a line of black olives. Break up the tuna and arrange in the center of the potato salad. Drizzle with dressing. Garnish with parsley and serve.