Put the potatoes in a large saucepan of lightly salted water and bring to the boil. Cook for 12–15 minutes until tender. Drain well and transfer to a large bowl. Cut any large potatoes in half.
Whisk the oil, vinegar and a little salt and pepper together in a small bowl. Add half to the potatoes, stir well and leave to cool completely.
Add the pine nuts, the remaining dressing and basil, stir well and serve.