Place the potatoes in a pan of boiling salted water, cover and simmer for 15–18 minutes, until just tender. Drain and leave to cool completely, then cut lengthways into quarters.
Place the eggs in a small pan and just cover with boiling water, then cook for 6 minutes. Drain and rinse under cold running water, then remove the shells and cut each egg in quarters.
Plunge the French beans in a pan of boiling salted water and blanch for a minute or so, then drain and refresh under cold running water.
Arrange the lettuce leaves on plates or one large platter and add the potatoes, French beans, tomatoes and anchovies, if using. Scatter over the tuna, then add the quartered eggs, olives and torn basil.
To make the dressing, whisk together the extra virgin olive oil, lemon juice, mustard and maple syrup in a small bowl and season with a pinch of salt and plenty of pepper or shake together in a screw-topped jar. Drizzle over the salad to serve.