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Peel and roughly chop parsnips. Steam until quite tender, about 20 minutes. Drain and keep covered.
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While parsnips steam, prepare onions by cutting in half lengthwise and then slicing into thin half-moon slices.
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Heat olive oil in a skillet until hot then add onions. Sauté for 10 minutes, then add vinegar. Cook over low heat until browned and caramelized, about 20-25 minutes.
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When onions are nearly done, place butter in a small saucepan. Melt then cook over low heat until browned, about 5-7minutes.
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Place parsnips, cream and browned butter in a medium bowl and mash well with a potato masher or ricer. Add onions and thyme leaves and mix to incorporate. Season with salt and pepper. Serve hot