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Preheat the oven to 400 degrees.
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Toss the potatoes, shallots and garlic with olive oil and spread evenly on a sheet tray lined with nonstick foil. Season well with kosher salt and pepper.
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Roast, turning occasionally, until browned and potatoes can be easily pierced with a knife, about 30-40 mins.
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While the potatoes are roasting, fill a large saucepan with water and 2 tsps salt and bring to a boil. Add the green beans and blanch until just tender. Drain and then immerse the beans in a large bowl of ice water to stop the cooking. When they're cool, remove the beans and lay them out to dry on paper towels.
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When the roasted garlic cloves are cool enough to handle, squeeze the garlic out of the peel. In a small food processor or with a whisk, mix together the roasted garlic, mustard, chive, dill, creme fraiche, salt and pepper.
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Toss the potatoes, shallots and green beans with the dressing and serve warm or at room temperature.