Make the Vinaigrette: In a small bowl or glass jar with a tight-fitting lid, combine the extra-virgin olive oil, red wine vinegar, lemon juice, Dijon mustard, minced shallot, and garlic. Add the salt and pepper. Whisk vigorously or shake the jar until the dressing is fully emulsified and creamy. Set aside.

Cook the Potatoes: Place the halved potatoes in a medium pot and cover with cold, salted water. Bring to a boil and cook for 10-15 minutes, or until just tender. Drain well and, while still warm, toss them with 2 tablespoons of the vinaigrette.

Cook the Eggs: Bring another small pot of water to a rolling boil. Gently lower the eggs into the water and cook for 7 minutes for a jammy yolk or 10 minutes for a hard-boiled yolk. Immediately transfer the eggs to a bowl of ice water. Once cooled, peel and slice them in half.

Blanch the Green Beans: Bring a pot of salted water to a boil. Prepare a large bowl of ice water. Add the haricots verts to the boiling water and cook for 2-3 minutes, until bright green and crisp-tender. Immediately transfer them to the ice bath to shock them. Drain well once cooled.

Assemble the Salad: On a large platter, arrange a bed of the lettuce leaves. Arrange the dressed potatoes, blanched green beans, halved cherry tomatoes, and sliced red onions in separate sections.

Add the Proteins: Break the oil-packed tuna into large chunks and arrange it on the salad. Place the halved eggs around the platter. Drape anchovy fillets over the top, if using. Scatter the olives over the entire salad.

Dress and Serve: Just before serving, drizzle the remaining vinaigrette over the entire platter. Garnish with fresh parsley or chives and serve immediately.