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Boil the potatoes in salted water for 20 mins until just cooked, drain, then cool.
Cut the potatoes into chunks, then throw into a bowl with the shallots, capers and cornichons, if using. Add enough mayonnaise to bind, then mix together the olive oil and vinegar and add just enough to give a little sharpness to the salad. Stir in the finely chopped parsley and serve.