For the dressing: Whisk together the vinegar, mustard and garlic. Whisk in the oil, adding it in a thin stream. Taste, and add some lemon juice if the dressing isn't sharp enough. Season with salt and pepper.
For the salad: Toss the lettuce leaves with a very little bit of the dressing and the shredded basil, and arrange on a platter. Toss the green beans, potatoes, tomatoes and artichoke hearts separately in a bit of dressing, and arrange on the platter. Scatter the onions and olives on top. Arrange the eggs and anchovies on top. Season with fleur de sel and pepper.