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Place the sliced red onion in a small bowl and cover with cold water. Let it soak for 10 minutes to make it less pungent.
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Make the lemon-shallot vinaigrette. Combing the vinegar, Dijon mustard, honey, minced shallots, lemon juice and zest, thyme and black pepper in a small bowl. Drizzle in the olive oil, whisking constantly. Whisk until the vinaigrette comes together and has thickened. Season to taste with salt and stir in the chives.
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Bring 2 quarts of water to a boil in a medium saucepan. Season the water with salt and boil the potatoes for about 10 to 12 minutes until they are tender to a knife point. Remove the potatoes from the pot with a slotted spoon and rinse the potatoes with cold water. Toss them with a few tablespoons of the vinaigrette and set aside to cool.
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Set up an ice water bath. Drop the haricot verts into the boiling water and blanch them for 5 minutes. Drain the beans and drop them into the ice water bath to stop them from over cooking. Drain the beans and pat them dry. Drizzle with some of the vinaigrette.
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Arrange the lettuce leaves on a large platter. Build your composed salad by keeping each ingredient together in groups. Arrange the potatoes, haricot verts, cherry tomatoes and black olives on top of the lettuce leaves. Flake the tuna apart gently with a fork and add it to the center of the platter, spreading it out a little between the vegetables. Slice the hardboiled eggs in half and add them along with the red onions to the platter.
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Generously drizzle the remaining vinaigrette over everything on the platter making sure you lightly cover all the ingredients. Season the salad with some sea salt and freshly ground black pepper. Tear off some fresh oregano leaves and sprinkle them on top of the salad. Serve immediately with salad tongs and let everyone help themselves. If desired, you can also divide up the ingredients and build individual servings on separate plates.