To cook the potatoes, add them to a saucepan and cover by 2 inches with cold water. Add salt, bring to a boil, and cook until soft but not falling apart.
In a jar combine the dressing ingredients, and shake until creamy and emulsified. In a large bowl, toss the potatoes with ¼ of the dressing.
To arrange the salad on a serving platter, add the lettuce, followed by the seasoned potatoes, green beans, cherry tomatoes, onions, tuna chunks, olives, and finally the eggs.