Boil the potatoes in their skins, rinse, peel and leave to cool.
Halve the olives and halve the red onions and cut into fine rings. Finely dice the pecorino cheese.
Cut the potatoes into large cubes and place in a large salad bowl.
Chop the parsley and finely chop the basil. Add to the bowl with the olives, onions and pecorino.
Prepare a salad dressing from the olive oil, white balsamic vinegar, salt and freshly ground pepper and add to the salad. Mix everything together thoroughly. Leave to rest in a cool place before serving.