In a jar or small bowl, combine the olive oil, lemon juice (or red wine vinegar), chopped shallot, basil, thyme, oregano (or tarragon), Dijon mustard, salt, and pepper. Cover and shake (or whisk) until fully blended.
Toss the red onion slices with 3 tablespoons of the vinaigrette in a small bowl. Let them sit while you prep the rest—this takes the edge off their bite.
In a large pot, cover the potatoes with 2 inches of water, add a tablespoon of salt, and bring to a boil. Lower to a simmer and cook for 10–12 minutes, until you can pierce them with a fork. Drain, cut into halves or quarters, then toss the warm pieces with about ¼ cup of the vinaigrette. Set aside.
Meanwhile, bring a pot of salted water to a boil. Add the green beans and cook for 3–5 minutes, until tender‑crisp. Drain and rinse under cold water (or plunge into an ice bath) to stop cooking.
If using tuna steaks, sear or grill them to your liking, then slice into ½‑inch pieces. If you’re using canned tuna, simply drain it.
Spread the torn lettuce over a large platter. Pile the tuna in the center. Arrange the dressed potatoes and green beans in neat piles around the tuna. Scatter the tomato wedges, marinated onions, egg quarters, olives, and anchovies (if using) over the greens.
Drizzle the remaining vinaigrette over the entire platter. Sprinkle with capers and chopped parsley if you like. Serve immediately at room temperature (or slightly warm) and enjoy!