Place the eggs in a saucepan and cover them with water. Bring to a boil, then simmer for approximately 9–12 minutes until hard-boiled. Transfer them to cold water, allow them to cool, peel, and cut them into halves or quarters.
If using potatoes, wash them thoroughly and place them in a saucepan of salted water. Simmer for approximately 10–15 minutes, or until fork-tender. Drain, allow them to cool slightly, and cut them into halves or bite-sized pieces.
Bring a saucepan of salted water to a boil. Add the trimmed green beans and cook for 3–5 minutes until tender-crisp. Drain immediately and transfer them to cold water to preserve their bright green color. Drain thoroughly.
Wash and dry the lettuce, tomatoes, cucumber, and radishes. Tear the lettuce into bite-sized pieces, cut the tomatoes into wedges, slice the cucumber, and thinly slice the red onion. Arrange the prepared ingredients separately for easy assembly.
In a small bowl, whisk together the olive oil, red wine vinegar, Dijon mustard, minced garlic, lemon juice, salt, and black pepper. Continue whisking until the dressing is well combined. Taste and adjust the acidity or seasoning as needed.
Drain the canned tuna and gently break it into large flakes using a fork. Keep some larger pieces intact so the salad has a pleasant texture. If desired, season lightly with black pepper and a little lemon juice.
Spread the lettuce leaves over a large serving platter or divide them among four individual plates. The lettuce creates a fresh base for the remaining ingredients.
Arrange the tomatoes, cucumber, green beans, red onion, radishes, and optional potatoes over the lettuce. Keep the ingredients in separate sections for a traditional platter-style presentation.
Place the flaked tuna and hard-boiled eggs over the vegetables. Scatter the olives around the platter and add anchovy fillets if desired. Sprinkle with fresh parsley for extra color and flavor.
Drizzle the Dijon vinaigrette over the salad just before serving. Alternatively, serve the dressing on the side so everyone can add the amount they prefer. Enjoy immediately while the vegetables remain fresh and crisp.