Boil the new potatoes in salted water until tender, about 15 minutes. Drain and cool.
Blanch the green beans briefly in boiling water, then immediately plunge into ice water to keep crispness and color. Drain well.
If using fresh tuna, sear quickly on each side in a hot skillet with olive oil until just cooked on the outside but still juicy inside. Let rest. If using canned tuna, drain and reserve some olive oil for flavor.
Cook eggs in simmering water for 9-11 minutes to hard-boiled texture. Cool in ice water, then peel and slice.
In a bowl, whisk together Dijon mustard, lemon juice, olive oil, anchovy paste, salt, and pepper until emulsified to make the vinaigrette.
On a large platter or bowl, arrange the potatoes, green beans, cherry tomatoes, olives, anchovy fillets, and tuna.
Top with sliced hard-boiled eggs, drizzle with the dressing, and garnish with fresh herbs before serving.