Wash and rub the potatoes clean, then put them in a pan of lightly salted water and bring to the boil. Simmer for about 15 minutes, until tender. Drain, and cut them in half if they're too big.
Meanwhile, put the rest of the ingredients into a mini food processor and blitz until you get a coarse paste. Season to taste with salt and pepper - adjust the lemon, oil & cheese to your liking.
When the potatoes are drained, put them in a serving dish and pour over the pistou immediately.
You can serve it warm or at room temperature.