For the dressing: whisk together the garlic, vinegar, and mustard. Whisk in the oil, adding it in a thin stream. Taste, and add some lemon if the dressing isn’t sharp enough. Season with salt and pepper. Set aside.
To serve: toss the lettuce leaves with a very little bit of the vinaigrette and the shredded basil, and arrange on a platter. Toss the tomatoes, potato slices, green beans and artichoke hearts separately in a bit of vinaigrette, and arrange on the platter. Scatter over the onion and olives. Arrange the eggs on top. Season with salt and pepper, and eat.