Place potatoes in a pot of cold salted water. Bring to a gentle boil and cook until fork-tender, about 15-20 minutes. Cool completely before slicing into ¼-inch rounds.
Prepare an ice bath. Bring another pot of heavily salted water to a boil. Add green beans and blanch for 2-3 minutes until bright green and crisp-tender. Immediately transfer to the ice bath to stop cooking. After 1-2 minutes, drain thoroughly and pat dry.
If using salad greens, arrange them as a base layer on a serving platter or individual plates.
Artfully arrange the potato slices, green beans, cherry tomatoes, olives, tuna chunks (flaked gently with a fork), and egg quarters on the platter.
For the dressing, whisk together olive oil, lemon juice, Dijon mustard (if using), salt, and freshly ground black pepper in a small bowl.
Drizzle the dressing evenly over the arranged salad. For best flavor, allow the dressing to settle for 5-10 minutes before serving.
If using optional ingredients like red onion, anchovies, herbs, or capers, scatter them across the salad just before serving.
