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Bring a pot of salted water to a boil.
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Add a pinch of sugar and the potato pieces.
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Cook until the potatoes are still firm but you can easily run a fork through them.
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Drain and set aside.
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In a small bowl, whisk together the mayonnaise, mustard, and lime juice.
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Grate the radishes and add to the mayonnaise mixture. Set aside.
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Place the parsley, dill, chives, olive oil, and water in a food processor and pulse until pureed.
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Season to taste with kosher salt and freshly ground black pepper.
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Place the potatoes and the herb puree in a bowl and toss together.
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Mix in the shallot rings
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Spoon the radish mayo on top.
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Alternately, toss to combine completely with the radish mayo.
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Garnish with extra fresh chopped herbs and serve.