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Tip the potatoes into a large pan of cold salted water. Bring to the boil, then simmer for 10 mins until tender to the tip of a knife.
While the potatoes are cooking, whisk the mustard, vinegar, olive oil and chopped shallot together with a good pinch of salt and a grind of pepper. When the potatoes are cool enough to handle, peel if you prefer, then halve, quarter or cut them into bite-sized chunks if large, then toss in the mustard dressing until completely coated. Leave to cool completely.
Meanwhile, mix the mayonnaise, soured cream, lemon juice and horseradish together. When the potatoes are cool, toss them through the mayonnaise mixture along with the spring onions. Tip into a dish and scatter with the crispy onions just before serving, or serve the crispy onions on the side for sprinkling over at the table.