Cook the potatoes and green beans separately: Bring a large pot of salted water to a boil. Add the halved new potatoes and cook for about 10 minutes, or until tender but still firm. Drain the potatoes and let them cool slightly.
In a separate pot, cook the green beans in boiling salted water for about 3-4 minutes, or until crisp-tender. Drain the green beans and immediately rinse them under cold water to stop the cooking process and keep them bright green.
Prepare the hard-boiled eggs: While the potatoes and beans are cooking, place the eggs in a small saucepan and cover them with cold water. Bring to a boil, then reduce the heat and simmer for 9 minutes. Remove the eggs, place them in cold water to cool, then peel and quarter them.
Make the vinaigrette: In a small bowl, whisk together the Dijon mustard, apple cider vinegar, olive oil, salt, and black pepper until well combined. Adjust seasoning to taste.
Assemble the salad: On a large serving platter or individual plates, arrange the mixed lettuce leaves as the base. Scatter the cooked potatoes, green beans, cherry tomatoes, red bell pepper slices, and artichoke hearts (if using) over the lettuce.
Add the protein: Flake the tuna into chunks and place it over the salad. Arrange the quartered hard-boiled eggs, anchovy fillets (if using), black olives, and capers on top.
Drizzle with vinaigrette: Just before serving, drizzle the vinaigrette evenly over the salad. Toss lightly if desired, or serve as is for a more composed presentation.
Serve immediately: This salad is best enjoyed fresh. Serve it as a main course or as a hearty side dish.